Math Problem Statement
Solution
We are given the function:
We are asked to find the derivative .
Step-by-step solution:
-
Derivative of : This is a composite function, so we will use the chain rule.
The chain rule states that the derivative of is:
For , we have:
- , so
Applying the chain rule:
-
Derivative of :
The derivative of is simply 1.
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Combine the results:
Now, sum the derivatives:
Final answer:
Would you like more details on any of the steps? Here are some related questions for practice:
- What is the derivative of ?
- How would you apply the chain rule to ?
- What is the derivative of ?
- How does the chain rule apply to functions like ?
- Find the second derivative of .
Tip: When using the chain rule, always differentiate the "inner" and "outer" functions separately and then multiply them together.
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Chain Rule
Formulas
Chain Rule: d/dx [g(x)^n] = n * g(x)^(n-1) * g'(x)
Theorems
Chain Rule
Suitable Grade Level
Grades 10-12
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