- Видео 31
- Просмотров 94 102
Yeah Math Is Boring
Добавлен 12 окт 2023
Our life is already hard, don't make it harder.
Are math problems keeping you up at night? Do you find equations and formulas confusing? Yeah, I know math is kinda boring and could be challenging at the same time. You're not alone, and I understand the struggle. Here, we dive into the world of math with empathy and clarity. Join me as I break down complex concepts, solve problems step by step, and make math more approachable. Whether you're a student, a lifelong learner, or just someone looking to conquer their math fears, this channel is for you. Let's make math a friend, not a foe, together!
#math #maths #mathematics #calculus #differentiation #integration #differential #integral
Are math problems keeping you up at night? Do you find equations and formulas confusing? Yeah, I know math is kinda boring and could be challenging at the same time. You're not alone, and I understand the struggle. Here, we dive into the world of math with empathy and clarity. Join me as I break down complex concepts, solve problems step by step, and make math more approachable. Whether you're a student, a lifelong learner, or just someone looking to conquer their math fears, this channel is for you. Let's make math a friend, not a foe, together!
#math #maths #mathematics #calculus #differentiation #integration #differential #integral
How to Find Limits by Direct Substitution?
How to find limit by direct substitution. In this video, we will go through some examples in finding the limit at a point of a function by using direct substitution. However, direct substitution cannot be used to find the limit if we end up with 0/0, which is an indeterminate form. Instead, conjugate method must be used in this case.
Conjugate Method Explanation:
ruclips.net/video/p-N5j5OPmJw/видео.html
#calculus #limits
TIMECODES:
0:00 First Example
0:56 Second Example
1:31 Third Example
1:49 Situation where direct substitution fails
Conjugate Method Explanation:
ruclips.net/video/p-N5j5OPmJw/видео.html
#calculus #limits
TIMECODES:
0:00 First Example
0:56 Second Example
1:31 Third Example
1:49 Situation where direct substitution fails
Просмотров: 274
Видео
How to Find Limits by Conjugate Method (Rationalizing)
Просмотров 180Месяц назад
How to find limits by conjugate method, or rationalizing? In this video, we will discover how to apply the conjugate or rationalizing method in finding the limits for a function. We will also discuss when we should use the conjugate, or rationalizing method. We use the conjugate method, or known as rationalizing, when direct substitution fails. Direct substitution fails when we plug the value o...
Finding Derivative from First Principles (Step-by-step Explanation)
Просмотров 170Месяц назад
How to find derivative by first principle? In this video, we will discuss how to take the derivative of a polynomial from first principles, also known as the limit definition, or the first definition. Normally, we use power rule to differentiate a polynomial function. First principle is the actual definition of differentiation in taking the derivative, and we will find the derivative of the fun...
How to take the derivative of csc x? (2 Different Methods)
Просмотров 1862 месяца назад
We will discover how to differentiate csc x, or as known as cosec x. According to the formula for derivatives, the derivative of csc x, or cosec x, is equal to - csc x cot x. In this video, we will apply 2 different methods to take this derivative, which are the quotient rule and the chain rule. The reason we can apply the quotient rule is that csc x = 1/sin x, where we have a quotient of funct...
Formula Derivation for First Principle of Derivatives
Просмотров 2232 месяца назад
In this video, we will discover how the formula for first principle of derivatives is derived, which is the formula derivation for the first principle. This is also known as the limit definition, or the first definition. So, how to derive the formula for the first principle of differentiation? For a given function represented by a curve, we plot two different points lying on it. We first find t...
How to take the derivative of tan x?
Просмотров 3752 месяца назад
We will discover how the derivative of tan x ends up being sec^2 x. Before we begin solving, we know that tan x is the same as sin x/cos x. Therefore, we can rewrite the equation, and continue solving it using the quotient rule. TIMECODES: 0:00 Intro 0:13 Rewrite equation 0:34 Applying Quotient Rule 1:11 Simplifying expression 2:20 Final Answer #derivatives #calculus #differentiation
How to Differentiate e^2x?
Просмотров 1,2 тыс.4 месяца назад
What is the derivative of e^2x? As e^2x is a composite function, we will be using the chain rule to find its derivative. For taking the derivative of an exponential function using the chain rule, we just have to copy back the exact same thing as our original function, then multiply it by the derivative of its exponent. In this case, we get 2e^2x as our final answer. #derivatives #differentiatio...
![How to integrate tan x? [2 Methods]](http://i.ytimg.com/vi/hrIS3rBSoIA/mqdefault.jpg)
How to integrate tan x? [2 Methods]
Просмотров 6 тыс.4 месяца назад
We will be discovering the 2 methods of integrating tan x in this video. The first method is by substitution, whereas the second method is by formula. We will get ln |sec x| C as our final answer. #integration #integral #calculus TIMECODES: 0:00 Intro 0:11 First Method - By Substitution 2:23 Second Method - By Formula 4:35 Outro
How to Differentiate sin^2 (x) ?
Просмотров 4,1 тыс.5 месяцев назад
What is the derivative of sin^2 (x)? We know that the derivative of sin x is equal to cos x. To solve the derivative of sin^2 x, we must know that it is actually a composite function, and we apply the chain rule in order to find the derivative of a composite function. We first differentiate the whole term without changing the inner function, and then multiply it by the derivative of the inner f...
How to find the derivative of logarithmic functions?
Просмотров 1,4 тыс.6 месяцев назад
Why is the general formula for the derivative of log x equal to 1/(x ln 10)? In this video, we will be discovering the derivative of logarithmic functions. First, by eliminating the common logarithm, we change the base of the logarithm to base e, which is natural logarithm. This is done to simplify the differentiation process. Then, the derivative can be found easily by using quotient rule, imp...
How to Differentiate x^x ? [2 Different Methods]
Просмотров 16 тыс.6 месяцев назад
There are 2 different ways to take the derivative of x^x, which are implicit differentiation, and the chain rule. In this video, we will be solving for the derivative of y=x^x by using these two methods. For the implicit differentiation, we first take the natural log on both sides of the equation, and we are able to apply implicit differentiation to solve for the derivative. For the chain rule,...
How to Differentiate ln(ln(ln(ln x))) ?
Просмотров 1,1 тыс.7 месяцев назад
This is a function that consists of the composition of functions within a composite function, so the chain rule is applied here to find the derivative. We apply the Chain Rule for three times in this case. CHAIN RULE EXPLANATION: ruclips.net/video/js8jOoWyZ2M/видео.html TIMECODES: 0:00 Into 0:10 Composite Function within Composite Function 0:28 Applying Chain Rule 0:59 Chain Rule 2nd time 1:26 ...
How to Integrate ln(x)?
Просмотров 15 тыс.8 месяцев назад
What is the integral of ln x? We apply integration by parts to solve this because it is a product of functions, where ln x multiply by 1 dx. We first select ln x as 'u', and 1 dx as 'dv'. Then, we take the derivative of 'u' in terms of dx, and take the integral of 'dv'. Finally, plug them into the formula of integration by parts and we got ' x ln(x) - x C ' as our final answer. #integration #in...
How to Differentiate e^e^x ?
Просмотров 1,7 тыс.8 месяцев назад
What is the derivative of e^e^x? This is a composite function, so we apply the chain rule to take the derivative of e^e^x. By applying the chain rule, we first differentiate the whole function without changing the inner function. Then, multiply it by the derivative of the inner function. In other words, when we are trying to take the derivative of an exponential function using the chain rule, w...
How to Differentiate ln(ln(ln x)) ?
Просмотров 2,3 тыс.8 месяцев назад
What is the derivative of ln(ln(ln x))? This is a composite function that involves multiple functions within it. It contains a composite function inside a composite function. Therefore, solve this using Chain Rule Differentiation for a total of two times. First, differentiate the whole function. Then, multiply it by the derivative of the inner function. And repeat it for one more time. CHAIN RU...
How to Differentiate Number Raised to Power of x?
Просмотров 4,5 тыс.8 месяцев назад
How to Differentiate Number Raised to Power of x?
Learn Implicit Differentiation Under 3.9667 Minutes!
Просмотров 1,3 тыс.9 месяцев назад
Learn Implicit Differentiation Under 3.9667 Minutes!
Learn Chain Rule Differentiation Under 3.6167 Minutes!
Просмотров 6879 месяцев назад
Learn Chain Rule Differentiation Under 3.6167 Minutes!
Integration By Parts Full Explanation in 4 minutes
Просмотров 9 тыс.9 месяцев назад
Integration By Parts Full Explanation in 4 minutes
Quotient Rule Differentiation Explained in 1 Minute
Просмотров 3449 месяцев назад
Quotient Rule Differentiation Explained in 1 Minute
Product Rule Differentiation Explained in 1 Minute
Просмотров 4999 месяцев назад
Product Rule Differentiation Explained in 1 Minute
Quickest Way for Limit at Infinity WITHOUT Dividing Every Terms
Просмотров 2359 месяцев назад
Quickest Way for Limit at Infinity WITHOUT Dividing Every Terms
not a fan of lawn. just call it log. log = ln. if the base is not e, then say log base b. we just get rid of bases not e anyway in most applications.
You did an excellent job!
Could you please send soft copy of above video
Good effort. Very brief and apt. Thank you.
Here it doesnt matter but sometimes it is good idea to choose a constant other than zero when we calculate v from dv
so simple and beautifull explanation !
Not really, it is when you know "everything" you have this. It depends how you build the function log(x) At start , you have exp(x) which is a function who exp(x)'=exp(x)... You are happy, it is the only one like so. You see exp(x)=e^x, it gives you e=2.718... A) One way for log definition Now , you are searching primitive for x^n where n is an integer (positive or negative). It is for polynomials primitives and for 1/x^n if n>0 . (x^n)'=n*x^(n-1) , You have primitve too any n : if f(x)=x^n ... F(x)=1/(n+1)*x^(n+1). Your are very happy , for any n you have a primitive. But you have a problem , it is not ok for n=-1. You dont have a primitive for 1/x with this method ! So you say : OK, I will call log(x) the primitive of 1/x (the good one with log(1)=0). In fact HERE log(x)'=1/x because it is définition of log(x) !!! Then proove exp(x) and log(x) are reciprocal functions... B) Second way : the way used in this video. You say log(x) is the reciprocal of exp(x) : definition of log(x) Then you calculate log(x)'=1/x. Conclusion : there is 2 ways possible to create log(x) : reciprocal of exp(x) or primitive of 1/x. It is a choice. The result is the same.
0:39 How come d/dx(e^y) become e^y(dy/dx) ? Where did the y come from?
That's the chain rule.
Thanks for a clearly detailed explanation 🎉🎉
Thanks for making this, these videos really do help people out!!
I'm preparing for my exams, and I wanted to give praise to your explanation. You presented this topic in a very clear and intuitive way for people to understand. Very well!
What if it is e^x(x²)dx Do i set u to x² And dv to e^xdx
I have a question
Anyway thnkx so I got problem why u conjugate numerator instead of conjugating denominator x
It depends on situations. We actually want to get rid of the square root, so we multiply the fraction by the conjugate of the expression that has a square root. For example, if the square root is in the numerator, we multiply it by the conjugate of numerator instead of denominator.
Thank u
No problem
How about integrating "sin 2x"?
sad this wasn't a fish to the fish video :(
Your animations are amazing How do you make them?
Microsoft PowerPoint
please make more videos on integration
I love this!
1/2 is it right?
Amazing explaination broo👏👏 Please keep making these videos they are very helpful
Thanks! I'll try my best
How you make this animations?
PowerPoint
This is the first video on RUclips that am commenting on, but woow, your explanation is on another level. Thanks please, much appreciated.
Glad to hear that!
next video -> why d(e^x) = e^x*dx
... The 2nd indeterminate limit can also be solved as follows ... in this case rewriting the numerator x - 5 as (4 + x) - 9 , and considering this expression as a difference of 2 squares ... (4+ x) - 9 = (SQRT(4 + x) - 3)(SQRT(4 + x) + 3) ... then cancelling common factor SQRT(4 + x) - 3 between top and bottom, giving us a solvable limit form in return ... lim(x->5)[SQRT(4 + x) + 3] = 6 ... solving this limit by factoring and cancelling ... thank you for your clear and instructive presentations ... take good care, Jan-W
❤❤
... Good day to you, Another way of solving your indeterminate limit, is to rewrite the denominator x in its original form as follows ... x = (4 + x) - 4 , and then treating this expression as a difference of 2 squares ... (SQRT(4 + x) - 2)(SQRT(4 + x) + 2) to finally cancelling the common factor (SQRT(4 + x) - 2) between numerator and denominator, to be left with a solvable limit form ... lim(x->0)[1/(SQRT(4 + x) + 2) = 1/4 ... solving by factoring I think I would call this ... thanks for sharing your instructive math channel with us, the interested viewers ... best wishes, Jan-W
Excellent explanation
Thanks!
Very great work, perfect explanation
Glad to hear that! I appreciate it!
Don't know how much you have to pay for AI voice, but you should consider switching even if you have to pay a bit more. Get an AI voice that knows a little math. "ln" is not "lawn" as in "mow the lawn". Once or twice might be charming but the whole video is about ln so "lawn" gets quickly annoying. Mike
That is how it is pronounced
God bless you
Thank you
No worries!
You don’t need to say it’s lnx times 1 lol just let dv = dx
You're right! I was just intended to provide a better clarification and understanding.
@@YeahMathIsBoring right I know but I don’t think it does
dv is just the rest of what’s left over
Since IBP is taught as a method for integrating products of functions is good to mention it at least though
@@coreymonsta7505 Yup, cuz some might think that lnx is just a single logarithmic term and they're confused why IBP is applied here
In the case of a pure inverse function, the integration by parts formula can be derived from the graph: int x dy=x*y-int y dx
1:07 Why all that talk 🤣 we know that eⁿ = x remplace it
Use first principles.
You kids get off my lawnx!
Can this be a method to prove the f'?
Absolutely! You can prove the derivative of f(x), which is denoted as f'(x) using the first principle of derivatives. In fact, first principle is the actual definition of differentiation, and the power rule that we normally use is actually derived from this formula.
Hard matn😅
but if we look at x^3, wouldn't y= x+1 be a tangent to x^3 at x = 3 be x+24? The slope of x + 24 is 1 but with differentiation, slope of tangent = 2*3^2 = 2*9 = 18?
If a line intersects the curve at only one point but does not have the same slope as the curve at that point, it is not a tangent line. It would simply be a line intersecting the curve at that point. The key aspect of a tangent line is that it is aligned with the curve's slope at the point of contact. I totally agree with you where by using differentiation, even with the first principle, we get our gradient function as 2x^2. If x=3, then 2(3)^2 would be 18, meaning that the gradient of the tangent line is 18 when x equals 3.
Thanks for making me understand more about this topic. I would like to ask does chain rule applied to all implicit equations? And if not, in what situation we can use it?
Yes it does! To clarify, chain rule is applied the on terms that have composition of functions, in which we differentiate the outer function without changing the inner function, and we then multiply it by the derivative of the inner function.
@YeahMathIsBoring would like to clarify more about on terms?
@@aziqasri5435 For example: (2x-1)^2, this term can be said that it has a composition of functions. But how? We let f(x) = x^2, and g(x) = 2x -1. When we plug in g(x) into f(x), which is denoted by f(g(x)), it would be (2x-1)^2. Notice that it is exactly the same as the original term. Therefore, we can say that f(g(x)) is a composite function, and that's why (2x-1)^2 can be said that it is a term that has a composition of functions. You may check out the video I uploaded to learn more about this in the chain rule topic: ruclips.net/video/js8jOoWyZ2M/видео.html
@YeahMathIsBoring thanks again, good sir. Anyway, I have subscribed to you.
@@aziqasri5435 Glad to hear that! I appreciate it!
"lawn y"
Can we take the derivative using power rule by applying dy/dx=sin x *sin x?
You can use product rule as y = sin x * sin x
Very comprehensive explanation
Thanks!
to the point explanation very great.
Glad to hear that! I've put everything I have into this explanation video.
Quotient rule...
Also from cos^2(x)+sin^2(x)/cos^2(x) we get 1+tan^2(x) which is by identity of sec^2(x)-tan^(x)=1, we have sec^2(x).
Amazing , just keep on posting more stuff
Thanks! I will try my best
Can this be done by implicit differentiation?
It's indeed possible actually. You'll first have to apply natural logarithmic on both sides of the equation.
Tq sir ❤...
Welcome