Question

How do you find the derivative of `y = x^4(2x - 5)^6`?

Answer 1

`y'=u'v+v'u`- product rule

Explanation:

Let `u=x^4` and `v=(2x-5)^6`
`u'=4x^3`
`v'=2*6(2x-5)^5=12(2x-5)^5->`by chain rule

Subbing into `y'=u'v+v'u`,

`y'=4x^3(2x-5)^6+12(2x-5)^5x^4`

Simplifying,

`y'=x^3(2x-5)^5(4(2x-5)+12x)=x^3(2x-5)^5(20x-20)`