Question

Differentiate the following function with respect to x:

(x+1)^3*(2x^2+3)*(x+3)^1/2
--------------------------
(x-4)^4

That's a fraction and the question hint says "Use logs".

Answer 1

yeah i bet it does
this is a nightmare

Answer 2

\[f(x)=\frac{(x+1)^3(2x^2+3)(x+3)^{1/2}}{(x-4)^4}\]\[\ln(f(x))=3\ln(x+1)+\ln(2x^2+3)+\frac{1}{2}\ln(x+3)-4\ln(x-4)\]

Answer 3

now taking the derivative is very easy
of course you are taking the derivative of the log, so for your final answer you will have to multiply by the original function

Answer 4

thank you so much