Derivative Formulas and Rules Through Unit 2 and Unit 3

Vocabulary flashcards covering differentiation formulas and rules from Unit 2 and Unit 3, including basic rules, trigonometric, exponential, logarithmic, inverse, and inverse trigonometric derivatives.

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

$$0$$

$$\frac{d}{dx}[c \cdot f(x)]$$

$$c \cdot f'(x)$$

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

$$n x^{n-1}$$

$$\frac{d}{dx}[f(x) + g(x)]$$

$$f'(x) + g'(x)$$

$$\frac{d}{dx}[f(x) - g(x)]$$

$$f'(x) - g'(x)$$

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

$$e^x$$

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

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

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

$$f'(x) g(x) + f(x) g'(x)$$

$$\frac{d}{dx}\left[\frac{f(x)}{g(x)}\right]$$

$$\frac{g(x) f'(x) - f(x) g'(x)}{(g(x))^2}$$

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

$$\cos(x)$$

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

$$-\sin(x)$$

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

$$\sec^2(x)$$

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

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

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

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

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

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

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

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

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

$$(\ln(a))(a^x)$$

Derivative of inverse function $g'(x)$ where $g(x)$ is the inverse of $f(x)$

$$g'(x) = \frac{1}{f'(g(x))}$$

$\frac{d}{dx}[f(g(x))]$ (Chain Rule)

$$f'(g(x)) g'(x)$$

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

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

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

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

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

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

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

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