find f(x).\nf(x) = ln x^4 + 7 ln x\nf(x) = \n
find f(x).\nf(x) = ln x^4 + 7 ln x\nf(x) = \n
Answer
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:
$\frac{11}{x}$