Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
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Question

Given f(x,y) = 2cosx·sin²y + y³/x², compute f_xy(x,y)
Options
A -2sinx·sin²y-2y³/x³
B -2sinx·sin2y-6y²/x³
Correct Answer
C -2cosx·sin²y+6y³/x⁴
D 2cosx·sin2y+3y²/x²
Correct Answer

Option B is the correct answer.

Detailed Explanation

Differentiate f_x=-2sinx sin²y-2y³/x³ with respect to y: d/dy[-2sinx sin²y]=-2sinx·sin2y, and d/dy[-2y³/x³]=-6y²/x³. Summing gives -2sinx·sin2y-6y²/x³.

Hint

Take f_x from the earlier question and differentiate it once more, this time with respect to y.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 839 of 930
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