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MTH 102 Practice Questions MTH 102 Objective Question
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Question

Differentiate e^(5x²+1) + 4^(cos3x) with respect to x
Options
A 10xe^(5x²+1) - 3sin3x·ln(4)[4^(cos3x)]
Correct Answer
B 10xe^(5x²+1) + sin3x·ln(4)[4^(cos3x)]
C 10xe^(5x²+1) - 3sin3x[4^(cos3x)]
D 10e^(5x²+1) - 3cos3x·ln(4)[4^(cos3x)]
Correct Answer

Option A is the correct answer.

Detailed Explanation

d/dx[e^(5x²+1)] = 10x·e^(5x²+1) by the chain rule. For 4^(cos3x), use d/dx[a^u] = a^u·ln(a)·u'; here u=cos3x, u'=-3sin3x, giving -3sin3x·ln4·4^(cos3x).

Hint

Apply the chain rule to each term separately: exponential-of-a-function and base-4-to-a-function.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 813 of 930
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