How do you differentiate f(x)=(3x^3-2x^2+5)^331?

1 Answer
Oct 11, 2016

(dy)/(dx)=331(9x^2-4x)(3x^3-2x^2+5)^330

Explanation:

Using chain rule: (dy)/(dx)=(dy)/(du)*(du)/(dx)

In this case, y=(3x^3-2x^2+5)^331

Let u=3x^3-2x^2+5,

then (dy)/(du)=331u^330 and (du)/(dx)=9x^2-4x

So (dy)/(dx)=331u^330*(9x^2-4x)

=331(9x^2-4x)(3x^3-2x^2+5)^330