Question

How do you use the chain rule to differentiate `y=(x^4+3x)^-2`?

Answer 1

`dy/dx=-(8x^3+6)/(x^4+3x)`

Explanation:

If `y=[f(x)]^n`

Then `dy/dx=n[f(x)]^(n-1)f'(x)`

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

`dy/dx=-2(x^4+3x)^-3(4x^3+3)=(-2(4x^3+3))/(x^4+3x)^3=-(8x^3+6)/(x^4+3x)^3`