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 $b$.