Find the derivative of the curve e^(xy) = sin(y)

First we have to identify that implicit differentiation is used to solve this question. We can differentiate the first the LHS first, by using the chain rule, we know that the differentiation of e^(xy) is e^(xy) times the differentiation of (xy). This becomes (y + xy') by using implicit differentiation. Sin(y) differentiates into y'cos(y). Rearranging the equation to get y' as the subject gives you (ye^(xy))/((cos(y)+xe^(xy))