Question

find f(x).
f(x)=6e^{x}+5x - ln x
f(x)= square

Explanation:

Step1: Differentiate each term separately.

The derivative of $a\cdot e^{x}$ is $a\cdot e^{x}$, the derivative of $ax$ is $a$, and the derivative of $\ln x$ is $\frac{1}{x}$.

Step2: Differentiate $6e^{x}$ term.

The derivative of $6e^{x}$ is $6e^{x}$ since the derivative of $e^{x}$ is $e^{x}$ and by the constant - multiple rule.

Step3: Differentiate $5x$ term.

The derivative of $5x$ is 5 as the derivative of $ax$ with respect to $x$ is $a$ (here $a = 5$).

Step4: Differentiate $-\ln x$ term.

The derivative of $-\ln x$ is $-\frac{1}{x}$ as the derivative of $\ln x$ is $\frac{1}{x}$.

Step5: Combine the derivatives.

$f'(x)=6e^{x}+5-\frac{1}{x}$

Answer:

$6e^{x}+5 - \frac{1}{x}$