Limits + Derivatives to know (AP Calc BC)

Some lImit and derivative definitions to know for AP Calc BC Class + AP exam

$$\frac{d}{\mathrm{d}x}\sin\left(x\right)$$

$$\cos\left(x\right)$$

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

$$-\sin\left(x\right)$$

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

$$\sec^2\left(x\right)$$

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

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

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

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

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

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

$$\frac{d}{dx}\frac{1}{x}$$

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

$$\frac{d}{dx}\sqrt{x}$$

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

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

$$e^{x}$$

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

$$a^{x}\ln\left(a\right)$$

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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