Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
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Question

Given f(x,y)=3tanx·log_ey - y²e^(3x), compute f_xx(x,y)
Options
A 3tanx/y - 2ye^(3x)
B 6log_ey sec²x tanx-9y²e^(3x)
Correct Answer
C 3sec²x log_ey-3y²e^(3x)
D -3tanx/y² - 2e^(3x)
Correct Answer

Option B is the correct answer.

Detailed Explanation

Differentiate f_x=3sec²x lny-3y²e^(3x) again with respect to x: d/dx[3sec²x lny]=3lny·2sec²x tanx=6lny sec²x tanx, and d/dx[-3y²e^(3x)]=-9y²e^(3x). Summing gives 6log_ey sec²x tanx-9y²e^(3x).

Hint

Differentiate f_x once more with respect to x, using d/dx[sec²x]=2sec²x tanx.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 909 of 930
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