Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
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Question

If y=x^(5x), find dy/dx
Options
A x^(5x)(1+lnx)
B 5x^(5x)lnx
C 5x^(5x)(1+lnx)
Correct Answer
D 5x^(5x)
Correct Answer

Option C is the correct answer.

Detailed Explanation

Take logs: ln y = 5x ln x. Differentiate implicitly: y'/y = 5lnx+5, so y'=5x^(5x)(1+lnx).

Hint

Use logarithmic differentiation since both the base and exponent involve x.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 872 of 930
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