Solving Derivative dy/dx: y, sin(xy) + 1 = cos x

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To solve the derivative dy/dx for the equation e^y * cos(x) = 1 + sin(xy), implicit differentiation is required. The initial attempt at differentiation yielded an incorrect result, indicating a misunderstanding of the application of the chain rule. The correct approach involves differentiating both sides of the equation while applying the product and chain rules appropriately. By carefully following these differentiation rules, one can derive the correct expression for dy/dx. Understanding these techniques is essential for successfully solving similar implicit differentiation problems.
skyhawk714
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1. Find the derivatie of y, dy when e/\(y) cos x=1 + sin (xy)
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dx

2. I don't know of any Relevant equations


3. The first time i tried the problem i got e/\(y) cos X+ y cos (xy)
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e/\(y) sin x- x cos (xy)

but i know that's not right...how do i even do a problem like this?
 
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You are trying to use implicit differentiation to find dy/dx given (e^y)*cos(x)=1+sin(xy), right? Your answer has the right sort of general form, but it's not correct. Differentiate both sides of (e^y)*cos(x)=1+sin(xy) using the chain rule and show the steps you did to get your answer.
 
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