Yes literally i am the student of class 8th and i just clicked on the video and i understood it very easily i would appreciate you to make these kinds of video that works on the grass root level of math that explains . The term "how " .😊
12 cuz, d/dx (x³) will be us using the exponent rule that states d/dx (x^n) = nx^(n-1),d/dx ( x³ ) = 3x^(3-1)= 3x² and input x = 2 it will be 3(2²) = 3(4) = 12 EDIT ; ( CORRECT ME IF IM WRONG )
if y'all want the first principles applied instead of the exponent rule thingy then ok let's do it let y= x³ then after we can use the formula lim h→0 [ ((x+h)³-x³)/h ] now we can't just add 0 on h and call it a day since anything/0 is undefined so we can try to transform this the identity (a+b)³=a³+3a²b+3ab² + b³ so knowing that let's use that to expand lil (x+h)³ this we'll end up to. lim h→0 [ (x³+3x²h+3xh²+h³-x³)/h ] we can cancel the two x³ in the numerator and factor h out lim h→0 [ h(3x²+3xh+h²)/h ] now cancel h on numerator and denominator lim h→0 [ 3x²+3xh+h² ] now let's use the property lim c→n ( f(x)±g(x)±p(x)...)= lim c→n [f(x)] ± lim c→n [g(x)] ± lim c→n [p(x) now we'll have 3 limits lim h→0 [3x²] + lim h→0 [3xh] + lim h→0 [h²] now do the first lim and using property lim m→n [ c ] = c (if c is a constant/not m) so we'll get lim h→0 [3x²] = 3x² cuz there is no h in this limit for the second and third we can put zero on the h's place so lim h→0 [3xh] = 3x0 which 0 multiplied by anything is zero or you can put 3x outside the limit but it'll still be zero like this 3xlim h→0 [h] = 3x0 and = 0 next is lim h→0 [ h²] which is 0² = 0 so all of that can equal to 3x²+0+0 which is 3x² and finally since brains station said if the value x = 2 then f(x) = 3x² f(2) = 3(2²) 2²= 2*2 f(2) = 3(4) f(2) = 12
3x²+3xh+h². At x=2, we get 12+6h+h² or h=[-6+/- (sqrt of 36-48)]/2 or h=[-6+/- 2i(sqrt 3)]/2 Thus, h= -3 +/- i(sqrt3) Sorry for showing unnecessary steps
You are right till 12+6h+h^2 After that you just have to set h as 0 and the answer would be 12.. That's it...you don't have to equate that equation of h to 0...just h=0
Enjoyed it? Part 3 coming soon 🔥 but you know the drill
Thanks!
For sure!!! I'm wainting for the Limits video!!
Sure pleasee
Please derive trigonometric derivatives, not all but some common ones
Yes literally i am the student of class 8th and i just clicked on the video and i understood it very easily i would appreciate you to make these kinds of video that works on the grass root level of math that explains .
The term "how " .😊
very super thank for the explanation.
12 cuz, d/dx (x³) will be us using the exponent rule that states d/dx (x^n) = nx^(n-1),d/dx ( x³ ) = 3x^(3-1)= 3x² and input x = 2 it will be 3(2²) = 3(4) = 12
EDIT ; ( CORRECT ME IF IM WRONG )
if y'all want the first principles applied instead of the exponent rule thingy then ok let's do it
let y= x³
then after
we can use the formula
lim h→0 [ ((x+h)³-x³)/h ]
now we can't just add 0 on h and call it a day since anything/0 is undefined so we can try to transform this
the identity
(a+b)³=a³+3a²b+3ab² + b³
so knowing that let's use that
to expand lil (x+h)³
this we'll end up to.
lim h→0 [ (x³+3x²h+3xh²+h³-x³)/h ]
we can cancel the two x³ in the numerator and factor h out
lim h→0 [ h(3x²+3xh+h²)/h ]
now cancel h on numerator and denominator
lim h→0 [ 3x²+3xh+h² ]
now let's use the property
lim c→n ( f(x)±g(x)±p(x)...)= lim c→n [f(x)] ± lim c→n [g(x)] ± lim c→n [p(x)
now we'll have 3 limits
lim h→0 [3x²] +
lim h→0 [3xh] +
lim h→0 [h²]
now do the first lim
and using property lim m→n [ c ] = c (if c is a constant/not m)
so we'll get
lim h→0 [3x²] = 3x² cuz there is no h in this limit
for the second and third we can put zero on the h's place
so lim h→0 [3xh] = 3x0 which 0 multiplied by anything is zero or you can put 3x outside the limit but it'll still be zero like this 3xlim h→0 [h] = 3x0 and = 0
next is lim h→0 [ h²] which is 0² = 0
so all of that can equal to
3x²+0+0
which is 3x²
and finally since brains station said if the value x = 2 then
f(x) = 3x²
f(2) = 3(2²) 2²= 2*2
f(2) = 3(4)
f(2) = 12
Your Explanation is Next level. ❤
Your Calculus series is lit 🔥Sir u are on fire! ❤ Thank u so much...I can watch it 1000 times ... it is sooo goood
Thanks a ton
9:56 derivative will be h² + 2x because h approaches 0 it will be 2x only
Thank you so much!
Answer for d(x³)/dx is 3x²
Given x=2
The answer would be 12
Can you please derive them all with this simple explanation
Needed this series❤
Wow
Call me isac
Cuz I invented calculus
Oh but the apple that hit my head made me restarted
3x^2?
Really calculid is love tnq sir love from india class 10th student ❤❤
If y=x³ then dy/dx(x=2)= 12
Bro can you explain little bit basic level sot hat i can understand
3x²+3xh+h². At x=2, we get 12+6h+h² or h=[-6+/- (sqrt of 36-48)]/2
or h=[-6+/- 2i(sqrt 3)]/2
Thus, h= -3 +/- i(sqrt3)
Sorry for showing unnecessary steps
You are right till 12+6h+h^2
After that you just have to set h as 0 and the answer would be 12.. That's it...you don't have to equate that equation of h to 0...just h=0
the answer to the question i think will be 12.
Sir please drop the snswer for y= x^3
May be its y = 3x^2??
The formula for that is x^n = nx^(n-1). 3x^2
@@trevorjames4619 sir is it applicable or valid in all that tyoe od derivatives
Sigma Boi
12 is the answer.
Derivative(x^2)=2x In other words D[x^2,x]=2x
1st comment 😎😎😎