How do you find the derivative of(x^5+x^6-8)^3?

1 Answer
Jul 18, 2018

Below

Explanation:

y=(x^5+x^6-8)^3

Let u=x^5+x^6-8
then (du)/(dx)=5x^4+6x^5

Since u=x^5+x^6-8, then
y=u^3
(dy)/(du)=3u^2

Therefore,
(dy)/(dx)=(dy)/(du)times(du)/(dx)
=3u^2times(5x^4+6x^5)
=3(x^5+x^6-8)^2(5x^4+6x^5)