Question

How do you find the derivative of `f(x)= [(2x-5)^5]/[(x^2 +2)^2]` using the chain rule?

Answer 1

`= (10(2x-5)^4*(x^2+2)^2 - (2x-5)^5*4x(x^2+2))/(x^2+2)^4`

Explanation:

`f'(x) = (f'(x) * g(x) - f(x) * g'(x))/(g(x))^2`

`f'(x) = (((5(2x-5)^4*2)(x^2+2)^2) - (2x-5)^5*(2(x^2+2)*2x))/((x^2+2)^2)^2`

`= (10(2x-5)^4*(x^2+2)^2 - (2x-5)^5*4x(x^2+2))/(x^2+2)^4`

You can reduce more, but it's bored solve this equation, just use algebraic method.