Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

If y = eax2+b, find dy/dx.
Options
A e<sup>ax<sup>2</sup>+b</sup>
B be<sup>ax<sup>2</sup>+b</sup>
C (a<sup>2</sup> + b)e<sup>ax<sup>2</sup>+b</sup>
D 2axe<sup>ax<sup>2</sup>+b</sup>
Correct Answer
Correct Answer

Option D is the correct answer.

Detailed Explanation

We are given y = eax2+b.To find the derivative dy/dx, we use the chain rule. The derivative of eu is eu * du/dx.Here, let u = ax2+b.Then, du/dx = d/dx (ax2+b) = a * 2x + 0 = 2ax.Applying the chain rule:dy/dx = eax2+b * (2ax) = 2ax eax2+b.This matches option D.

Hint

Remember the chain rule for exponential functions: d/dx [ef(x)] = ef(x) * f'(x).

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 310 of 930
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