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The question in the image asks:

**Q3. The derivative of log x with respect to x is:**

To solve this, we need to find the derivative of the natural logarithm function \( \log(x) \), which is commonly written as \( \ln(x) \) when referring to the natural log (logarithm with base \( e \)).

### Solution:
The derivative of \( \ln(x) \) with respect to \( x \) is given by:
\[
\frac{d}{dx} \ln(x) = \frac{1}{x}
\]

So, the derivative of \( \log x \) (assuming it is the natural logarithm) with respect to \( x \) is \( \frac{1}{x} \).

Would you like further details or clarifications on logarithmic derivatives? Here are some related questions:

1. What is the derivative of \( \log_b(x) \), where \( b \) is a base other than \( e \)?
2. How does the chain rule apply to composite logarithmic functions?
3. What is the integral of \( \frac{1}{x} \)?
4. Can you explain why the derivative of \( \ln(x) \) is \( \frac{1}{x} \)?
5. How do logarithmic properties affect their derivatives?

**Tip:** When dealing with logarithmic derivatives, always ensure you're clear on the base of the logarithm—whether it's natural (\( \ln \)) or any other base \( b \).

The derivative of log x with respect to x is?

Understand how to find the derivative of the logarithmic function log x with respect to x. This problem uses key calculus concepts, including differentiation and logarithmic functions. Suitable for students in Grades 11-12.

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