Math Problem Statement
Differentiate the function g(u) = √(3u) + √(2u).
Solution
We are given the function:
To find , we need to differentiate this expression with respect to .
Step-by-step solution:
-
Rewrite the square roots as exponents:
-
Apply the chain rule to differentiate each term:
- For , use the chain rule:
- For , similarly:
-
Combine the results:
Thus, the derivative of is:
Let me know if you would like further clarification or have any questions!
Here are some related questions to expand your understanding:
- How do you apply the chain rule to more complicated functions?
- What happens if you differentiate a product of functions involving square roots?
- How would you integrate the function ?
- What is the difference between implicit and explicit differentiation?
- How can the power rule be used to differentiate terms with fractional exponents?
Tip: Always check if functions can be simplified before differentiation—it often makes the process easier!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Differentiation
Chain Rule
Square Roots
Formulas
g(u) = √(3u) + √(2u)
Derivative of a square root: d/dx (√x) = 1/(2√x)
Chain Rule
Theorems
Chain Rule for Differentiation
Power Rule for Differentiation
Suitable Grade Level
Grades 11-12