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

1 Answer
Mauricio M.
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.

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