Differentiation Rules and Formulas

Vocabulary-style flashcards covering standard derivative rules for power, exponential, logarithmic, trigonometric, and inverse trigonometric functions.

$$\frac{d}{dx}(x^n)$$

$$nx^{n-1}$$

$$\frac{d}{dx}(e^x)$$

$$e^x$$

$$\frac{d}{dx}(b^x)$$

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

$$\frac{d}{dx}(\ln(x))$$

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

$$\frac{d}{dx}(\log_b(x))$$

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

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

$$\cos(x)$$

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

$$-\sin(x)$$

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

$$\sec^2(x)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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