Question

find ( f(x) ).
( f(x)=2 e^{x}+3 x-ln x )

Explanation:

Step1: Differentiate term by term

Differentiate $2e^x$, $3x$, and $-\ln x$ separately.

Step2: Derivative of $2e^x$

$\frac{d}{dx}(2e^x) = 2e^x$ (since derivative of $e^x$ is $e^x$)

Step3: Derivative of $3x$

$\frac{d}{dx}(3x) = 3$ (power rule: $\frac{d}{dx}(kx) = k$)

Step4: Derivative of $-\ln x$

$\frac{d}{dx}(-\ln x) = -\frac{1}{x}$ (derivative of $\ln x$ is $\frac{1}{x}$)

Step5: Combine derivatives

Add the results of each term's derivative.

Answer:

$2e^x + 3 - \frac{1}{x}$