To find $f'(x)$ for the function:

$f(x) = 7e^x + 5x - 3\ln(x)$

We differentiate each term separately:

1. The derivative of $7e^x$ is $7e^x$ (since the derivative of $e^x$ is $e^x$).
2. The derivative of $5x$ is $5$.
3. The derivative of $-3\ln(x)$ is $-\frac{3}{x}$ (since the derivative of $\ln(x)$ is $\frac{1}{x}$).

Thus, the derivative $f'(x)$ is:

$f'(x) = 7e^x + 5 - \frac{3}{x}$

Would you like more details or have any questions?

Here are 5 related questions you can explore:

1. What is the derivative of $e^x$ in general?
2. How do we apply the chain rule for more complex logarithmic functions?
3. What is the derivative of $\ln(x)$ with different coefficients?
4. How does the constant rule affect differentiation?
5. What is the relationship between exponential and logarithmic derivatives?

Tip: Always remember to apply the power rule when differentiating terms like $x^n$ (for $n \neq 0$).