Math Problem Statement
If f'(-3) = -10, and g(x) = -8f(x), what is g'(-3)?
Solution
We are given the following information:
We need to find .
Step 1: Differentiate
Given , we can differentiate both sides of this equation with respect to .
Step 2: Plug in the value
Substitute into the derivative we just found:
Final Answer:
Would you like more details or have any further questions?
Here are some related questions to consider:
- How do we differentiate functions using the chain rule?
- What does it mean to differentiate a function like ?
- How do we apply the product rule in cases with more complicated products?
- What happens when functions have constants multiplied by them?
- Can we use this method for other composite functions?
Tip: When differentiating a function multiplied by a constant, the constant remains and you only differentiate the variable function.
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Math Problem Analysis
Mathematical Concepts
Differentiation
Function Derivatives
Calculus
Formulas
g'(x) = -8f'(x)
Theorems
Derivative of a function multiplied by a constant
Suitable Grade Level
Grades 11-12