Answer to Question #269320 in Calculus for Angel Nodado

Question

Find dy.

3. sin(xy) = x ^ 2 - y

Answer 1

$\displaystyle \sin(xy)=x^2 -y\\ \text{Differentiating implicitly, we have}\\ y\cos(xy)+x\cos(xy)\frac{dy}{dx}= 2x-\frac{dy}{dx}\\ \text{Collecting like terms, we have }\\ \frac{dy}{dx}(x\cos(xy)+1)= 2x-y\cos(xy)\\ \implies \frac{dy}{dx} = \frac{2x-y\cos(xy)}{x\cos(xy)+1}$