Question Detail
Question
Given f(x,y) = 2cosx·sin²y + y³/x², compute f_y(x,y)
Correct Answer
Option D is the correct answer.
Detailed Explanation
Treating x as constant: d/dy[2cosx sin²y]=2cosx·2siny cosy=2cosx·sin2y, and d/dy[y³/x²]=3y²/x². Summing gives 2cosx·sin2y+3y²/x².
Hint
Hold x fixed and differentiate each term with respect to y only, using sin²y → 2siny·cosy = sin2y.