How do you differentiate # y =cos^3(5x^2-2)# using the chain rule?

1 Answer
Jun 15, 2017

Answer:

# dy/dx = -30x \ cos^2(5x^2-2) \ sin(5x^2-2) #

Explanation:

We have:

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

We will need two application of the chain rule:

# d/dx u^3 \ \ \ = 3u^2 (du)/dx #
# d/dx cosv = -sinv (dv)/dx #

Thus we get:

# dy/dx = 3cos^2(5x^2-2) * (-sin(5x^2-2) ) * (10x) #
# \ \ \ \ \ = -30x \ cos^2(5x^2-2) \ sin(5x^2-2) #