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To solve the derivative of \( 10^x \), we can use the general rule for differentiating exponential functions of the form \( a^x \), which is:

\[
\frac{d}{dx}(a^x) = a^x \ln(a)
\]

Here, \( a = 10 \). Therefore, the derivative of \( 10^x \) is:

\[
\frac{d}{dx}(10^x) = 10^x \ln(10)
\]

So, the correct answer from the given options is **D: \( 10^x \ln(10) \)**.

Would you like more details on how to differentiate exponential functions or have any further questions?

Here are some related questions:
1. How do you differentiate general exponential functions like \( a^x \)?
2. What is the derivative of \( e^x \) and how does it compare to \( a^x \)?
3. Can you explain how logarithms come into play when differentiating exponentials?
4. How would you apply the chain rule to derivatives of exponential functions like \( 10^{f(x)} \)?
5. How can you differentiate expressions involving both exponents and logs, like \( \ln(10^x) \)?

**Tip**: Remember that for bases other than \( e \), the natural logarithm \( \ln(a) \) appears in the derivative!

What is the derivative of 10^x with respect to x?

Explore how to differentiate the exponential function 10^x using the formula d/dx (a^x) = a^x * ln(a). This solution explains step-by-step how to apply the derivative rules for exponential functions. Suitable for advanced high school students in Grades 11-12.

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