The derivative of \( 6\sin(x) \) with respect to \( x \) is:

\[
\frac{d}{dx} [6\sin(x)] = 6\cos(x)
\]

This result follows from the basic derivative rule that the derivative of \( \sin(x) \) is \( \cos(x) \), and the constant multiple rule.

Would you like more details or have any further questions? 

Here are some related questions you might find interesting:

1. What is the derivative of \( 6\sin(2x) \)?
2. How do you find the second derivative of \( 6\sin(x) \)?
3. What is the integral of \( 6\sin(x) \)?
4. What is the derivative of \( \sin^2(x) \)?
5. Can you explain the product rule for derivatives?

**Tip**: The chain rule is essential when differentiating composite functions like \( \sin(2x) \).

Understand how to find the derivative of 6sin(x) with this step-by-step solution. Learn the application of the constant multiple rule and the derivative of trigonometric functions. Ideal for students in Grades 11-12.

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