Calculus 1 help urgently

Question

Calculate the derivative of the function:

Calculate the derivative of the function:

𝑓(𝑥)=((𝑥^5−4)/(𝑥+9))^−4

Answer: 𝑓′(𝑥)=  

Answer 1

It is easier if you rewrite the function

f(x) = ((x⁵-4)/(x+9))^-4 = ((x+9)/(x⁵-4))⁴ = (g(x)/h(x))⁴

Then use the chain and quotient rules.

f '(x)= 4(g(x)/h(x))³((g'(x)h(x)-h'(x)g(x))/(h(x))²