# Find the derivative of the following function

## Homework Statement

y = cos^3(5x^2-6)

## The Attempt at a Solution

I used the chain rule for this question but im not sure about the cos^3 part. Using the chain rule i got

-10xSin^3(5x^2-6)

But was I supposed to use the power rule on the cos^3 part? I can think of 3 ways this could be done but im not sure which way to go about it.

Thanks!

You have to think of both cosine AND the exponent 3 as external functions. So you need to perform the chain rule twice:

(d/dx) cos^3(5x^2-6) = 3 (cos(5x^2-6))^2 * (d/dx) cos(5x^2-6), at which you point you'll also need to do the chain rule cos(5x^2-6).

How do I do the chain rule twice with this?

I got 3 Cos(5x-6)^2 by -sin (5x^2-6)?

Do I do something like ( 3 (-sin (5x^2-6) d/dx (5x^2-6))^2 ) (-sin (5x^2-6)

?

I think I was making this too complicated.

=d/dx Cos^3 d/dx (5x^2-6)
=3Cos^2(5x^2-6) -sin(5x^2-6) 10x
=-30xCos^2(5x^2-6)Sin(5x^2-6)

What do you guys an gals think?

Gib Z
Homework Helper
That is correct.