Math Problem Statement
For the following exercises, find f’(x) for each function. f(x)= x2 ln 9x
Solution
To find the derivative for the function , we can use the product rule and chain rule.
Step-by-step process:
Given:
We recognize that this is the product of two functions:
1. Differentiate using the product rule:
The product rule states: So:
2. Differentiate :
3. Differentiate :
To differentiate , use the chain rule:
4. Apply the product rule:
Simplify the second term:
Thus, the derivative of is:
Would you like more details or have any questions?
Here are 5 related questions for practice:
- Differentiate .
- Find for .
- Differentiate .
- What is the derivative of ?
- Find the derivative of .
Tip: When differentiating products of functions, always remember the product rule formula .
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Math Problem Analysis
Mathematical Concepts
Differentiation
Product Rule
Chain Rule
Logarithmic Functions
Formulas
Product Rule: (fg)' = f'g + fg'
Chain Rule: (ln(9x))' = 1/x
Theorems
Product Rule
Chain Rule
Suitable Grade Level
Grades 11-12, Early College