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 $\sin(2x)$.