Unit 2 & 3 (AP Calc BC)

log_bx

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

where functions are NOT differentiable

corners and cusps, discontinuities, vertical tangents

e^x

$$e^{x}$$

$$b^{x}$$

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

$$\ln x$$

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

$$\sin x$$

$$\cos x$$

$$\cos x$$

$$-\sin x$$

$$\tan x$$

$$\sec^2x$$

$$\csc x$$

$$-\csc x\cot x$$

$$\sec x$$

$$\sec x\tan x$$

$$\cot x$$

$$-\csc^2x$$

$$\sin^{-1}x$$

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

$$\cos^{-1}x$$

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

$$\tan^{-1}x$$

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

$$\csc^{-1}x$$

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

$$\sec^{-1}x$$

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

$$\cot^{-1}x$$

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

$$f^{-1}x$$

$$\frac{1}{f^{\prime}\left(f^{-1}\left(x\right)\right)}$$

$$\lim_{x\to0}\frac{\sin x}{x}$$

1

$$\lim_{x\to0}\frac{\cos x-1}{x}$$

0