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3 sin(xy) = 7x + 5y

Taking derivatives of both sides:

3 d/dx ( sin(xy) ) = d/dx (7x + 5y)

Use the chain rule to differentiate the left hand side.

3 cos(xy) d/dx (xy) = 7 + 5 dy/dx

Use the product rule to differentiate (xy):

3 cos (xy) [y + x dy/dx] = 7 + 5 dy/dx

Now, you need to combine all the terms that have dy/dx:

3 y cos(xy) - 7 = [5 - 3x cos(xy) ] dy/dx

[3y cos(xy) - 7]/[5 - 3x cos(xy) ] = dy/dx

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