The derivative of \( a \cdot u^n \) with respect to \( u \), where \( a \) and \( n \) are constants, can be found using the **power rule** of differentiation.

The power rule states that the derivative of \( u^n \) with respect to \( u \) is \( n \cdot u^{n-1} \).

Thus, the derivative of \( a \cdot u^n \) is:

\[
\frac{d}{du}(a \cdot u^n) = a \cdot n \cdot u^{n-1}
\]

So, the derivative is:

\[
a \cdot n \cdot u^{n-1}
\]

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions to expand your understanding:

1. What is the derivative of \( a \cdot \sin(u) \)?
2. How do you apply the chain rule to \( a \cdot (u^n + v^m) \)?
3. How does the product rule apply if \( a \) is a function of \( u \) as well?
4. What is the second derivative of \( a \cdot u^n \)?
5. How do you integrate \( a \cdot u^n \)?

**Tip**: Always double-check if the constants or functions involved depend on the variable you're differentiating with respect to!

Discover how to find the derivative of a*(u^n) using the power rule. This calculus problem involves differentiating with respect to u, applying the power rule, and understanding constants in differentiation. Perfect for students in Grades 10-12 looking to solidify their understanding of basic differentiation techniques.

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