Math Problem Statement
Diketahui f(x) = x + 1 dan g(x) = x^2 - 1. Rumus fungsi (f/g)'(x) adalah ....
Solution
The question asks for the formula for the derivative of the division of two functions, and , where:
To find , we use the quotient rule for differentiation:
Steps:
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Find :
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Find :
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Substitute into the quotient rule:
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Simplify the numerator:
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Final formula:
The derivative of is:
Would you like a more detailed explanation of any step? Here are five related questions to consider:
- How is the quotient rule applied to general functions and ?
- Why is it necessary to calculate both and ?
- How do we simplify the numerator in the quotient rule?
- Can this formula be further factorized or simplified?
- What happens if at certain points?
Tip: Always double-check your simplifications, especially in the numerator, to ensure the final formula is correct!
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Math Problem Analysis
Mathematical Concepts
Quotient Rule
Differentiation
Formulas
Quotient Rule: (f/g)'(x) = [f'(x)g(x) - f(x)g'(x)] / [g(x)]^2
Theorems
Differentiation rules
Suitable Grade Level
Grades 10-12