Derivatives with Chain Rule

The Chain Rule is a formula for computing the derivative of the composition of two or more functions. It states that if you have a function $$y = f(g(x))$$ , then the derivative is given by $$\frac{dy}{dx} = f'(g(x)) \times g'(x)$$ .

$$\frac{dy}{dx}=-\frac{2}{x^3}$$ .

$$\frac{dy}{dx}=\frac{1}{g(x)} \times g'(x)$$ .

$$\frac{dy}{dx}=\frac{2}{x}$$ .

You use the Chain Rule when there is a function within another function.

$$\frac{dy}{dx}=\frac{6x+1}{3x^2+x}$$ .

$$\frac{dy}{dx}=-2xe^{3-x^2}$$ .

$$\frac{dy}{dx}=e^{g(x)} \times g'(x)$$ .

$$\frac{dy}{dx}=\text{cos}(g(x)) \times g'(x)$$ .

$$\frac{dy}{dx}=-\text{sin}(g(x)) \times g'(x)$$ .