find f(x). f(x) = ln x^{10}+5 ln x f(x) =
find f(x). f(x) = ln x^{10}+5 ln x f(x) =
Answer
Explanation:
Step1: Simplify the function
Use the logarithm property $\ln a^b = b\ln a$. So, $f(x)=\ln x^{10}+5\ln x = 10\ln x+5\ln x=15\ln x$.
Step2: Differentiate the simplified function
The derivative of $\ln x$ is $\frac{1}{x}$. Using the constant - multiple rule $(cf(x))' = cf'(x)$ where $c = 15$ and $f(x)=\ln x$, we have $f'(x)=15\times\frac{1}{x}$.
Answer:
$\frac{15}{x}$