AP Calc Unit 2 Review

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

$$nx^{n-1}$$

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

$$0$$

$$\frac{d}{dx}\left\lbrack f\left(x\right)\cdot g\left(x\right)\right\rbrack$$

$$g\left(x\right)\cdot f^{\prime}\left(x\right)+f\left(x\right)\cdot g^{\prime}\left(x\right)$$

$$\frac{d}{dx}\left\lbrack\frac{f\left(x\right)}{g\left(x\right)}\right\rbrack$$

$$\frac{g\left(x\right)\cdot f^{\prime}\left(x\right)-f\left(x\right)\cdot g^{\prime}\left(x\right)}{\left\lbrack g\left(x\right)\right\rbrack^2}$$

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

$$\cos(x)$$

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

$$-\sin(x)$$

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

$$\sec^2(x)$$

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

$$\sec\left(x\right)\cdot\tan\left(x\right)$$

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

$$f^{\prime}\left(g\left(x\right)\right)\cdot g^{\prime}\left(x\right)$$

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

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

$$\frac{d}{dx}\sin^{-1}\left(u\right)$$

$$\frac{u^{\prime}}{\sqrt{1-u^2}}$$

$$\frac{d}{dx}\tan^{-1}\left(u\right)$$

$$\frac{u^{\prime}}{1+u^2}$$

$$\frac{d}{dx}\sec^{-1}\left(u\right)$$

$$\frac{u^{\prime}}{\left|u\right|\sqrt{u^2-1}}$$

$$\frac{d}{dx}\log_{a}\left(u\right)$$

$$\frac{u^{\prime}}{u\cdot\ln\left(a\right)}$$

$$\frac{d}{dx}\ln\left(u\right)$$

$$\frac{u^{\prime}}{u}$$

$$\frac{d}{dx}a^{u}$$

$$\ln\left(a\right)\cdot a^{u}\cdot u^{\prime}$$