Question

How do you use the chain rule to differentiate `y=(4x^5-1)root3(x+1)`?

Answer 1

`y=20x^4(x+1)^(1/3)+(4x^5-1)/(3(x+1)(2/3))`

Explanation:

We use the product rule
`(uv)'=u'v+uv'`
and the chain rule

`(f(g(x))'=f'(g(x))*g'(x)`
to get
`y'=20x^4(x+1)^(1/3)+(4*x^5-1)*(1/3)(x+1)^(-2/3)`