Question

find f(x).
f(x) = ln x^4 + 7 ln x
f(x) =

Explanation:

Step1: Use logarithm property

First, use the power - rule of logarithms $\ln x^n=n\ln x$. So, $\ln x^4 = 4\ln x$. Then $f(x)=4\ln x + 7\ln x$.

Step2: Combine like terms

Combine the two $\ln x$ terms. $f(x)=(4 + 7)\ln x=11\ln x$.

Step3: Differentiate

The derivative of $\ln x$ is $\frac{1}{x}$. Using the constant - multiple rule of differentiation $(cf(x))'=cf'(x)$ where $c = 11$ and $f(x)=\ln x$, we get $f'(x)=11\times\frac{1}{x}$.

Answer:

$\frac{11}{x}$