How to take the derivative? (30 problems focusing on the first step)

How do we take the derivative? Here we will go over 30 typical calculus 1 derivative problems and focus on the differentiation step. This video will help you master the derivative techniques including the power rule, product rule, quotient rule, chain rule, implicit differentiation, and more!
Here's the free file: / calc-1-focus-on-113341690
Answer key: / calc-1-focus-on-113341988
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[@jrhabqgduwha396]

Now I know all about The Box

[@Hjominbonrun]

Yes, this is a good video.
Teaching math is not about solving the entire problem and taking long time to simplify.
It should be about teaching patterns, techniques and showing applications of rules.
I teach my son by showing him 100 problems and he has to talk to me to tell me what he sees on each problem and what he plans to do.
Not waste time multiplying decimals.

[@frylockfromathf9592]

This came just in time for my derivatives test so talk about awesome timing thank you!

[@leaf647]

Every time I hear you say box I suffer less, thank you

[@anonymouscheesepie3768]

1. e^(sqrt(x)) * 1/(2sqrtx) = e^sqrt(x)/(2sqrt(x))
2. sec(x^2 + x)tan(x^2 + x) * (2x + 1) = (2x + 1)sec(x^2 + x)tan(x^2 + x)
3. (cosx(1 + cosx) + sin^2x)/(1 + cosx)^2 = (cosx + 1)/(1 + cosx)^2 = 1/(1 + cosx)
4. 2xtanx + x^2sec^2x

[@omograbi]

I don't have access to Patreon from my countrey, could you please share the link via other clouds?

[@perekman3570]

Some countries block Patreon? That's just evil.

[@danielkovacs6809]

Always The Box.
It's like a mathematical horror movie.

[@EliteKoji_1215]

Is there any need to further simplify the answer ?

[@matheusvivan3434]

The GOAT

[@done3500]

Please take this👑

[@SarojtapashLalita]

I got all 30 right
Is it enough
Can I assume I have passed calc 1 derivative

[@Lukrafiveman]

Wheres the derivative table?

[@bprpcalculusbasics]

That is also in the first Patreon link. You just need to be a free member to access it.

[@Lukrafiveman]

@@bprpcalculusbasics Thanks

[@eustacenjeru7225]

So cool

[@GabrielDeBorja]

Some are not simplified

[@Kotuseid]

Yay

[@zactastic4k955]

Now differentiate e^ln(sin(arcsin(x))) no simplification

[@carultch]

Given:
e^(ln(sin(arcsin(x))))
Assign the function names, f(x), g(x), h(x), and p(x), to show the chain rule process:
f(x) = e^x
g(x) = ln(x)
h(x) = sin(x)
p(x) = arcsin(x)
Corresponding derivatives:
f'(x) = e^x
g'(x) = 1/x
h'(x) = cos(x)
p'(x) = 1/sqrt(1 - x^2)
First chain rule:
d/dx h(p(x)) = h'(p(x)) * p'(x)
Next chain rule:
d/dx g(h(p(x))) = g'(h(p(x))) * h'(p(x)) * p'(x)
Final chain rule:
d/dx f(g(h(p(x)))) = f'(g(h(p(x)))) * g'(h(p(x))) * h'(p(x)) * p'(x)
Thus:
d/dx e^(ln(sin(arcsin(x)))) =
e^(ln(sin(arcsin(x)))) * 1/(sin(arcsin(x))) * cos(arcsin(x)) 1/sqrt(1 - x^2)
As an exercise to you, this will simplify to 1. Which we expect, because your given function is all compositions of inverses, that ultimately simplifies to x.

[@alyme_r]

God revealed to me in a dream that the answer is 1.

[@Orillians]

@@carultch This literally feels like chatgpt write it 😭😭

[@guruone]

FullSimplify[RSolveValue[(f[x] - f[x - a])/a == 1 - 2 x f[x], f[x], x] /. C[1] -> 0 /. a -> 1/z] as z->Infinity
What is the function?