https://file.aiquickdraw.com/mathbot/file/1730247257990dpsplvia.jpg

To differentiate the function \( y = 7e^x + 2\ln(x) \), we will apply the rules for differentiation.

1. **Differentiate \( 7e^x \):**
   - The derivative of \( e^x \) is \( e^x \).
   - So, \( \frac{d}{dx}(7e^x) = 7e^x \).

2. **Differentiate \( 2\ln(x) \):**
   - The derivative of \( \ln(x) \) is \( \frac{1}{x} \).
   - So, \( \frac{d}{dx}(2\ln(x)) = 2 \cdot \frac{1}{x} = \frac{2}{x} \).

Now, combining both results:

\[
y' = 7e^x + \frac{2}{x}
\]

### Final Answer:
\[
y' = 7e^x + \frac{2}{x}
\]

Would you like further details or have any questions?

---

Here are some related questions to explore further:
1. How would you differentiate \( y = e^{3x} + \ln(x^2) \)?
2. What is the derivative of \( y = 5e^{x^2} \)?
3. How would you differentiate a function involving \( \ln(x) \) in the denominator?
4. How do the product and chain rules apply when differentiating exponential functions?
5. How do you find the second derivative of \( y = 7e^x + 2\ln(x) \)?

**Tip:** For logarithmic functions, remember that the derivative of \( \ln(x) \) is \( \frac{1}{x} \), which is especially useful when combined with constants or more complex expressions.

Differentiate the function y = 7e^x + 2ln(x)

Learn how to differentiate the function y = 7e^x + 2ln(x) with a step-by-step solution. This problem covers differentiation rules for exponential and logarithmic functions, suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation