Answer to Question #204087 in Calculus for moe

Question

Using imlicit differentiation, determine the derivative of $cos(x-2y) = sin(2x+y)$

Answer 1

$$\cos(x-2y)=\sin(2x+y)$$

Differentiate both sides with respect to $x$

$$\dfrac{d}{dx}(\cos(x-2y))=\dfrac{d}{dx}(\sin(2x+y))$$

Use the Chain Rule

$$-\sin(x-2y)(1-2\dfrac{dy}{dx})=\cos(2x+y)(2+\dfrac{dy}{dx})$$

Solve for $\dfrac{dy}{dx}$

$$\dfrac{dy}{dx}=\dfrac{\sin(x-2y)+2\cos(2x+y)}{2\sin(x-2y)-\cos(2x+y)}$$