Math Problem Statement
Find the derivative of the function g(x) = sin(6 - 7x).
Solution
To find the derivative of the function , we apply the chain rule.
- First, the derivative of is , where .
- Then, we take the derivative of the inner function , which is .
Thus, the derivative of is:
Would you like more details on how the chain rule was applied?
Here are five related questions you might find useful:
- What is the chain rule, and how is it applied in calculus?
- How do you differentiate trigonometric functions involving composite functions?
- How would the derivative change if the function was ?
- How do you differentiate a function involving multiple trigonometric terms?
- 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.
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Math Problem Analysis
Mathematical Concepts
Calculus
Differentiation
Trigonometry
Chain Rule
Formulas
d/dx[sin(u)] = cos(u) * du/dx
d/dx[6 - 7x] = -7
Theorems
Chain Rule
Suitable Grade Level
Grades 11-12