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

1 Answer
Apr 18, 2018

= (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.