Question Detail

MTH 102 Differentiation Objective Question
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Question

Find \( f'(x) \) for \( f(x) = \frac{x}{\sqrt{x^2 - 4}} \).
Options
A \( \frac{-4}{(x^2-4)^{3/2}} \)
Correct Answer
B \( \frac{x^2-4}{(x^2-4)^{3/2}} \)
C \( \frac{1}{\sqrt{x^2-4}} \)
D \( \frac{-4}{(x^2-4)^{1/2}} \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

Using quotient and chain rule: ( f'(x) = \frac{(1)\sqrt{x^2-4} - x\cdot\frac{1}{2}(x^2-4)^{-1/2}(2x)}{x^2-4} = \frac{x^2-4-x^2}{(x^2-4)\sqrt{x^2-4}} = \frac{-4}{(x^2-4)^{3/2}} ).

Hint

Use the quotient rule and simplify the resulting expression.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 117 of 930
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