Question Detail

MTH 102 MTH 102 Past Questions Objective Question
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Question

Which of the following option best is correct regarding differentiation rules?
Options
A d/dx [ln f(x)] = f’’(x)/f(x)
B d/dx [ln f(x)] = f’(x)/f(x)
Correct Answer
C d/dx [ln f(x)] = f(x)/f’(x)
D d/dx [ln f(x)] = f’(x)ln(f(x))
Correct Answer

Option B is the correct answer.

Detailed Explanation

To find the derivative of ln(f(x)), we use the chain rule.Let y = ln(u), where u = f(x).Then dy/du = 1/u and du/dx = f'(x).By the chain rule, dy/dx = (dy/du) * (du/dx) = (1/u) * f'(x).Substitute back u = f(x):dy/dx = (1/f(x)) * f'(x) = f'(x)/f(x).Option B correctly states this derivative rule.

Hint

Apply the chain rule for the derivative of a composite function involving the natural logarithm. The derivative of ln(u) is (1/u) * du/dx.

Question Info

Course: MTH 102
Topic: MTH 102 Past Questions
Type: Objective
Difficulty: Not specified
Question 390 of 930
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