Question

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

Answer 1

`(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`