The image shows the graph of the exponential function $f(x) = 2^x$, and you are asking for the derivative, $f'(x)$.

To differentiate $f(x) = 2^x$, we use the chain rule and the fact that the derivative of $a^x$ (for any base $a$) is given by: $\frac{d}{dx}(a^x) = a^x \ln(a)$ where $\ln(a)$ is the natural logarithm of the base $a$.

In the case of $f(x) = 2^x$, the derivative is: $f'(x) = 2^x \ln(2)$

Thus, the derivative of $f(x) = 2^x$ is $f'(x) = 2^x \ln(2)$.

Would you like further explanation or have questions about this?

Here are 5 related questions to expand on the concept:

1. How do you differentiate more complex exponential functions like $3^x$?
2. What is the difference between differentiating $2^x$ and $e^x$?
3. How does the graph of the derivative $f'(x) = 2^x \ln(2)$ compare to the graph of $f(x) = 2^x$?
4. Can you explain the chain rule in detail when applied to functions like $2^x$?
5. How do logarithmic functions relate to the differentiation of exponential functions?

Tip: When differentiating exponential functions with bases other than $e$, always remember to multiply by the natural logarithm of the base!