Question

find f(x). f(x)=3x - ln x^2 f(x)=□

Explanation:

Step1: Apply sum - difference rule

The derivative of a sum/difference of functions is the sum/difference of their derivatives. So $f'(x)=(3x)'-(\ln x^{2})'$.

Step2: Differentiate $3x$

The derivative of $ax$ with respect to $x$ is $a$. For $y = 3x$, $y'=3$.

Step3: Differentiate $\ln x^{2}$

Use the chain - rule. First, rewrite $\ln x^{2}=2\ln x$. The derivative of $\ln x$ is $\frac{1}{x}$, so the derivative of $2\ln x$ is $2\times\frac{1}{x}=\frac{2}{x}$.

Step4: Calculate $f'(x)$

$f'(x)=3-\frac{2}{x}$.

Answer:

$3-\frac{2}{x}$