Question

What is the derivative of `f(x)=ln[x^9(x+3)^6 (x^2+7)^5]`?

Answer 1

Use the properties of logarithms to rewrite:

`f(x)=ln[x^9(x+3)^6 (x^2+7)^5]`

`= ln(x^9)+ln(x+3)^6+ln(x^2+7)^5`

`= 9ln(x)+6ln(x+3)+5ln(x^2+7)`

So,

`f'(x) = 9/x+6/(x+3)+5/(x^2+7) 2x`

Simplify algebraically as desired.