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The derivative of the given function \( f(x) = x^2 \cdot 7^x \) is:

\[
f'(x) = 7^x \cdot x \cdot (x \ln(7) + 2)
\]

Would you like a more detailed explanation of the steps involved in differentiating this function?

Here are 5 related questions to expand on this concept:
1. How do you differentiate products of functions (Product Rule)?
2. What is the logarithmic differentiation technique and when is it useful?
3. How do you differentiate exponential functions like \( a^x \)?
4. What is the Chain Rule and how does it apply here?
5. How does the derivative change if the function is \( x^n \cdot a^x \), where \( n \) is any power?

**Tip:** Always identify when to use the product and chain rules when differentiating products involving exponential and polynomial functions.

Learn how to differentiate the function f(x) = x^2 * 7^x using the product rule and the properties of exponential functions. This problem involves key calculus concepts such as differentiation, the product rule, and the chain rule. Suitable for students in Grades 11-12 or early college.

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