Chapter 2 - Derivatives - 2.6 Implicit Differentiation - 2.6 Exercises - Page 166: 11

For $y\cos x=x^2+y^2$ find $\frac{dy}{dx}$ by implicit differentiation $\frac{dy}{dx}=\frac{2x +y\sin x}{\cos x-2y}$

Differentiate both sides with respect to $x$ $\frac{dy}{dx}\cos x-y\sin x=2x+2y\frac{dy}{dx}$ Isolate $\frac{dy}{dx}$ $\frac{dy}{dx}\cos x-2y\frac{dy}{dx}=2x +y\sin x$ $\frac{dy}{dx}(\cos x-2y)=2x +y\sin x$ $\frac{dy}{dx}=\frac{2x +y\sin x}{\cos x-2y}$