Derivative Rules

1-16

$$\frac{d}{dx}[c]$$

0

$$\frac{d}{dx}[x^{n}]$$

$$nx^{n-1}$$

$$\frac{d}{dx}[e^{x}]$$

$$e^{x}$$

$$\frac{d}{dx}[b^{x}]$$

$$b^{x}\ln(b)$$

$$\frac{d}{dx}[\ln(|x|)]$$

$$\frac{1}{x}$$

$$\frac{d}{dx}[\log_{b}(x)]$$

$$\frac{1}{x \ln(b)}$$

$$\frac{d}{dx}[\sin(x)]$$

$$\cos(x)$$

$$\frac{d}{dx}[\cos(x)]$$

$$-\sin(x)$$

$$\frac{d}{dx}[\tan(x)]$$

$$\sec^2(x)$$

$$\frac{d}{dx} [\cot(x)]$$

$$-\csc^2(x)$$

$$\frac{d}{dx} [\sec(x)]$$

$$\sec(x)\tan(x)$$

$$\frac{d}{dx} [\csc(x)]$$

$$-\csc(x)\cot(x)$$

$$\frac{d}{dx} [\sin^{-1}(x)]$$

$$\frac{1}{\sqrt{1 - x^2}}$$

$$\frac{d}{dx} [\cos^{-1}(x)]$$

$$-\frac{1}{\sqrt{1 - x^2}}$$

$$\frac{d}{dx} [\tan^{-1}(x)]$$

$$\frac{1}{x^2 + 1}$$

$$\frac{d}{dx} [\cot^{-1}(x)]$$

$$-\frac{1}{x^2 + 1}$$