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To find the derivative of the function \( g(x) = \sin(6 - 7x) \), we apply the chain rule.

1. First, the derivative of \( \sin(u) \) is \( \cos(u) \), where \( u = 6 - 7x \).
2. Then, we take the derivative of the inner function \( 6 - 7x \), which is \( -7 \).

Thus, the derivative of \( g(x) \) is:

\[
g'(x) = \cos(6 - 7x) \cdot (-7) = -7\cos(6 - 7x).
\]

Would you like more details on how the chain rule was applied?

Here are five related questions you might find useful:
1. What is the chain rule, and how is it applied in calculus?
2. How do you differentiate trigonometric functions involving composite functions?
3. How would the derivative change if the function was \( g(x) = \cos(6 - 7x) \)?
4. How do you differentiate a function involving multiple trigonometric terms?
5. Can you apply the chain rule to other non-trigonometric functions, like exponentials?

**Tip:** When differentiating composite functions, always start by identifying the "outer" function and apply the chain rule to account for the derivative of the "inner" function.

Find the derivative of the function g(x) = sin(6 - 7x).

Learn how to find the derivative of g(x) = sin(6 - 7x) using the chain rule. This problem demonstrates key calculus concepts, including differentiation of trigonometric functions and applying the chain rule. Suitable for Grades 11-12.

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