Question Detail

MTH 102 Differentiation Objective Question
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Question

Differentiate \( y = x^{2x} \).
Options
A \( x^{2x}(2 + 2\ln x) \)
Correct Answer
B \( 2x \cdot x^{2x-1} \)
C \( x^{2x} \ln x \)
D \( 2x^{2x} \)
Correct Answer

Option A is the correct answer.

Detailed Explanation

Use logarithmic differentiation: ( \ln y = 2x \ln x ). Differentiating gives ( \frac{1}{y} y' = 2\ln x + 2x(1/x) = 2\ln x + 2 ). So ( y' = y(2 + 2\ln x) = x^{2x}(2 + 2\ln x) ).

Hint

Take the natural logarithm of both sides before differentiating.

Question Info

Course: MTH 102
Topic: Differentiation
Type: Objective
Difficulty: Not specified
Question 127 of 930
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