Question

How do you use the chain rule to differentiate `f(x)=(x^9+3x^2-5x^-6+3x^4)^-3`?

Answer 1

`f'(x)=-(3(9x^8+12x^3+6x+30x^-7))/(x^9+3x^4 +3x^2-5x^-6)^4`

Explanation:

Chain rule:

`[f(x)]^n=n[f(x)]^(n-1)f'(x)`

`f(x)=(x^9+3x^2-5x^-6+3x^4)^-3`

`f'(x)=-3(x^9+3x^2-5x^-6+3x^4)^-4(9x^8+6x+30x^-7+12x^3)`

`f'(x)=-(3(9x^8+12x^3+6x+30x^-7))/(x^9+3x^4 +3x^2-5x^-6)^4`