Derivative Rules - Before Chain Rule Flashcards | Quizlet

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

$$\cos(x)$$

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

$$-\sin(x)$$

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

$$\sec^2(x)$$

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

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

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

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

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

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

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

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

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

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

What is $\frac{d}{dx}[c]$ for any constant $c$?

$$0$$

What is $\frac{d}{dx}[(x)]$?

$$1$$

What is $\frac{d}{dx}[(x^n)]$?

$$nx^{n-1}$$

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

$$cf'(x)$$

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

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

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

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

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

$$\frac{1}{x},\,x > 0$$

What is $\frac{d}{dx}[\log_b(x)]$?

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

What is $\frac{d}{dx}[mx + b]$?

$$m$$

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

$$e^x$$

What is $\frac{d}{dx}[ax^n]$?

$$anx^{n-1}$$

What is $\frac{d}{dx}\left[\frac{1}{x}\right]$?

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

What is $\frac{d}{dx}[\sqrt{x}]$?

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

What is $\frac{d}{dx}[\ln|x|]$?

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

What is $\frac{d}{dx}[-x]$?

$$-1$$

What is $\frac{d}{dx}[e^{-x}]$?

$$-e^{-x}$$

Which course is this set of derivative rules designed for?

AP Calculus AB