Question

How do you use the chain rule to differentiate `y=2(x^4+x)^-1`?

Answer 1

`y'=-2(x^4+x)^(-2)(4x^3+1)`
`y'=[-2(4x^3+1)]/(x^4+x)^(-2)`

Explanation:

`y=2(x^4+x)^(-1)`

Differentiate this using the chain rule , which in simplest terms, it means "Derivative of the outside times derivative of the inside".

`y'=-2(x^4+x)^(-2)(4x^3+1)`

We can write this as a rational function:
`y'=[-2(4x^3+1)]/(x^4+x)^(-2)`