Math Problem Statement
Jika y = √(2x + 6), maka y' = ...
Solution
Let's solve the problem in the image. The given equation is:
We are tasked with finding the derivative .
Step-by-step process:
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Rewrite the equation:
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Use the chain rule to differentiate:
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Differentiate :
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Combine the results: Simplifying further:
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Return the derivative to radical form:
Conclusion:
The correct answer is option a, which matches the derivative we calculated:
Would you like more details or have any questions? Here are some related problems you could explore:
- How do you apply the chain rule to more complex functions?
- What happens if the function inside the square root is more complicated?
- How do you differentiate higher powers of functions, like ?
- Can you use the product rule and chain rule together?
- What is the importance of simplifying derivatives after applying the chain rule?
Tip: When differentiating functions involving roots, rewriting them as fractional exponents makes it easier to apply the chain rule!
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Math Problem Analysis
Mathematical Concepts
Differentiation
Chain Rule
Algebra
Formulas
y = (2x + 6)^{1/2}
dy/dx = 1/2 * (2x + 6)^{-1/2} * d(2x+6)/dx
Theorems
Chain Rule
Suitable Grade Level
Grades 11-12