Find f prime left parenthesis x right parenthesis.
f left parenthesis x right parenthesis equals 7 e Superscript x Baseline plus 5 x minus 3 ln x


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 \( n \neq 0 \)).

Discover how to differentiate the function f(x) = 7e^x + 5x - 3ln(x) with this step-by-step guide. This problem involves key calculus concepts such as the chain rule, exponential functions, and logarithmic derivatives. Ideal for students in Grades 11-12 or early college.

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