Question

i need to find derivative of (cos^3)(2x^4)

Answer 1

You need to use the Product Rule in this one.

Answer 2

And Chain Rule as well.

Answer 3

The part I'm having trouble with is the first part (cos^3) Would I use the derivative of cos which would be -sin or leave it as cos....

Answer 4

first do the derivative of the power and then cosine function

Answer 5

Yup, that's the Chain Rule.

Answer 6

so before it's simplified would it look like:
(3(-sin^2) x (2x^4)) + (cos^3)(8x^3)

Answer 7

y r u using product rule?
we need to apply only chain rule here

Answer 8

I'm confused as to what the outer function and the inner function is to use the chain rule...

Answer 9

first do the derivative of power then cosine function
and after that term inside the cosine function
For example :-
we need to find the derivative of
\[y = \sin^2(4x)\]
first i m doing the derivative of power
y' = 2sin(4x)* {sin(4x)}'
= 2sin(4x) * cos(4x) * (4x)'
= 2sin(4x)* cos(4x) * 4
NOTE:- ' symbol denotes the first derivative w.r.t x

Answer 10

if 4x is raised to the 3rd power in your original equation, would that change the process? so 4x^3 would become 12x^2?