Use implicit differentiation to find dy/dx of the equation 3y^2 + 2^x + 9xy = sin(y).

Differentiating each term separately, and using implicit differentiation to differentiate the functions of y by differentiating with respect to y and multiplying by dy/dx, we can obtain 6ydy/dx + ln22^x + 9y + 9xdy/dx = cos(y)dy/dx. This involves using the product rule, and the rule that the derivative of a^x is lnaa^x. Once we have obtained this we need to move all the terms that are multiplied by dy/dx onto the same side so we can factor it out, i.e dy/dx(6y + 9x - cos(y)) = -9y - ln22^x. Finally by division, we obtain dy/dx = (-9y - ln2*2^x)/(6y + 9x -cos(y)).