DIFF EQ — Derivatives

$$\dfrac{d}{dx}[x^n]$$

$nx^{n-1}$

$$\dfrac{d}{dx}[f(x)g(x)]$$

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

$$\dfrac{d}{dx}\left[\dfrac{f(x)}{g(x)}\right]$$

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

$$\dfrac{d}{dx}[f(g(x))]$$

$$f'(g(x)) \cdot g'(x)$$

$$\dfrac{d}{dx}[e^x]$$

$e^x$

$$\dfrac{d}{dx}[a^x]$$

$$a^x \ln a$$

$$\dfrac{d}{dx}[\ln x]$$

$$\dfrac{1}{x}$$

$$\dfrac{d}{dx}[\log_a x]$$

$$\dfrac{1}{x \ln a}$$

$$\dfrac{d}{dx}[\sin x]$$

$$\cos x$$

$$\dfrac{d}{dx}[\cos x]$$

$$-\sin x$$

$$\dfrac{d}{dx}[\tan x]$$

$$\sec^2 x$$

$$\dfrac{d}{dx}[\csc x]$$

$$-\csc x \cot x$$

$$\dfrac{d}{dx}[\sec x]$$

$$\sec x \tan x$$

$$\dfrac{d}{dx}[\cot x]$$

$$-\csc^2 x$$

$$\dfrac{d}{dx}[\sin^{-1} x]$$

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

$$\dfrac{d}{dx}[\cos^{-1} x]$$

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

$$\dfrac{d}{dx}[\tan^{-1} x]$$

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

$$\dfrac{d}{dx}[\csc^{-1} x]$$

$$-\dfrac{1}{|x|\sqrt{x^2-1}}$$

$$\dfrac{d}{dx}[\sec^{-1} x]$$

$$\dfrac{1}{|x|\sqrt{x^2-1}}$$

$$\dfrac{d}{dx}[\cot^{-1} x]$$

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