Question

Find implicit differentiation of 2y+cot(xy^2)=3xy

Answer 1

$$F(x,y)=2y+\cot(xy^2)-3xy$$

$$y'(x)=-\frac{F'_x}{F'_y}=-\frac{-\frac{y^2}{\sin^2(xy^2)}-3y}{2-\frac{2xy}{\sin^2(xy^2)}-3x}$$

$$y'(x)=\frac{y^2+3y\sin^2(xy^2)}{2\sin^2(xy^2)-2xy-3x\sin^2(xy^2)}$$