$$\frac{d}{dx}\,x^n$$
$$nx^{n-1}$$
$$\frac{d}{dx}\,k$$
$$0$$
$$\frac{d}{dx}\,e^x$$
$$e^x$$
$$\frac{d}{dx}\,(f(x)\pm g(x))$$
$$f'(x)\pm g'(x)$$
$$\frac{d}{dx}\,k\cdot f(x)$$
$$k\cdot f'(x)$$
$$\frac{d}{dx}\,f(g(x))$$
$$ f'(g(x))g'(x)$$
$$\frac{d}{dx}\,(u\cdot v)$$
$$u’v+uv’$$
$$\frac{d}{dx}\,\Big(\frac{u}{v}\Big)$$
$$\frac{u’v-uv’}{v^2}$$
$$\frac{d}{dx}\,\sin{x}$$
$$\cos{x}$$
$$\frac{d}{dx}\,\cos{x}$$
$$-\sin{x}$$
$$\frac{d}{dx}\,\tan{x}$$
$$\sec^2{x}$$
$$\frac{d}{dx}\,\cot{x}$$
$$-\csc^2{x}$$
$$\frac{d}{dx}\,\sec{x}$$
$$\sec{x}\tan{x}$$
$$\frac{d}{dx}\,\csc{x}$$
$$-\csc{x}\cot{x}$$
$$\frac{d}{dx}\,e^x$$
$$e^x$$
$$\frac{d}{dx}\,\ln{x}$$
$$\frac{1}{x},\,x>0$$
$$\frac{d}{dx}\,\sin^{-1}{x}$$
$$\frac{1}{\sqrt{1-x^2}}$$
$$\frac{d}{dx}\,\cos^{-1}{x}$$
$$\frac{-1}{\sqrt{1-x^2}}$$
$$\frac{d}{dx}\,\tan^{-1}{x}$$
$$\frac{1}{1+x^2}$$
$$\frac{d}{dx}\,\sqrt{x}$$
$$\frac{1}{2\sqrt{x}}$$
$$\frac{d}{dx}\,\frac{1}{x}$$
$$-\frac{1}{x^2}$$