Question

find f(x).

f(x) = \ln x^{11} + 4 \ln x

f(x) = \square

Explanation:

Step1: Simplify the function

Use the logarithmic property $\ln x^n=n\ln x$. So, $f(x) = 11\ln x+4\ln x=(11 + 4)\ln x=15\ln x$.

Step2: Differentiate the function

The derivative of $\ln x$ is $\frac{1}{x}$. Using the constant - multiple rule $(cf(x))^\prime = cf^\prime(x)$ (where $c = 15$ and $f(x)=\ln x$), we have $f^\prime(x)=15\times\frac{1}{x}$.

Answer:

$\frac{15}{x}$