Question

find the derivative of f with respect to x of f(x) = ln x^2. the derivative of f with respect to x of f(x) = ln x^2 is

Explanation:

Step1: Use logarithm property

We know that $\ln x^{2}=2\ln x$ by the power - rule of logarithms $\ln a^{b}=b\ln a$.

Step2: Differentiate $2\ln x$

The derivative of $\ln x$ with respect to $x$ is $\frac{1}{x}$. Using the constant - multiple rule of differentiation $(cf(x))' = cf'(x)$ where $c = 2$ and $f(x)=\ln x$, we have $(2\ln x)'=2\times\frac{1}{x}=\frac{2}{x}$.

Answer:

$\frac{2}{x}$