Unit 3 Check (Implicit Differentiation)

$$x^4\cos\left(x\right)-4x^3\sin\left(x\right)$$  

$$x^4\cos\left(x\right)+4x^3\sin\left(x\right)$$  

$$4x^3\cos\left(x\right)$$  

$$-4x^3\cos\left(x\right)$$  

$$\left(3x^2-2\right)\cos\left(x^3-2x\right)$$  

$$-\left(3x^2-2\right)\cos\left(x^3-2x\right)$$  

$$\cos\left(3x^2-2\right)$$  

$$\sin\left(3x^2-2\right)$$  

$$x^2e^x$$  

$$x^2e^x-e^x$$  

$$xe^x-e^x$$  

$$xe^x$$  

1

$$-\sin x\cos x$$  

$$\cos^2x-\sin^2x$$  

$$\frac{2x}{y}$$  

$$\frac{x}{3y}$$  

$$\frac{3y}{2x}$$  

$$\frac{2x}{3y}$$  

$$\frac{dy}{dx}=5x-\frac{2}{x^2}$$  

$$\frac{dy}{dx}=-\frac{6x^2}{10y-5}$$  

$$\frac{dy}{dx}=-\frac{7}{y^2+5x}$$  

$$\frac{dy}{dx}=\frac{6x^2}{10y+5}$$  

$$\frac{dy}{dx}=\frac{x}{y}$$  

$$\frac{dy}{dx}=-\frac{x}{y}$$  

$$\frac{dy}{dx}=-\frac{x}{3y}$$  

$$\frac{dy}{dx}=\frac{x}{3y}$$