Table of Derivatives

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Power of x

$𝑑 𝑑 𝑥 (𝑐) = 0 𝑑 𝑑 𝑥 (𝑐 𝑥) = 𝑐 𝑑 𝑑 𝑥 (𝑐 𝑥 𝑛) = 𝑛 𝑐 𝑥 𝑛 - 1$

For example,
$𝑑 𝑑 𝑥 5 𝑥 3 = 3 \cdot 5 𝑥 2 = 15 𝑥 2$

You'll also want to remember that $1 𝑥 𝑛 = 𝑥 - 𝑛$ (for example, $1 𝑥 2 = 𝑥 - 2),$ and $𝑛 \sqrt 𝑥 = 𝑥 1 / 𝑛$ (example: $3 \sqrt 𝑥 = 𝑥 1 / 3$ ).

Exponential and Logarithmic

$𝑑 𝑑 𝑥 (𝑒 𝑥) = 𝑒 𝑥 𝑑 𝑑 𝑥 (𝑎 𝑥) = 𝑎 𝑥 l n 𝑎 𝑑 𝑑 𝑥 (l n 𝑥) = 1 𝑥 𝑑 𝑑 𝑥 (l o g 𝑎 𝑥) = 1 𝑥 l n 𝑎$

Trigonometric

$𝑑 𝑑 𝑥 (s i n 𝑥) = c o s 𝑥 𝑑 𝑑 𝑥 (c s c 𝑥) = - c s c 𝑥 c o t 𝑥 𝑑 𝑑 𝑥 (c o s 𝑥) = - s i n 𝑥 𝑑 𝑑 𝑥 (s e c 𝑥) = s e c 𝑥 t a n 𝑥 𝑑 𝑑 𝑥 (t a n 𝑥) = s e c 2 𝑥 𝑑 𝑑 𝑥 (c o t 𝑥) = - c s c 2 𝑥$

Inverse Trigonometric

$𝑑 𝑑 𝑥 (s i n - 1 𝑥) = 1 \sqrt 1 - 𝑥 2 𝑑 𝑑 𝑥 (c s c - 1 𝑥) = - 1 𝑥 \sqrt 𝑥 2 - 1 𝑑 𝑑 𝑥 (c o s - 1 𝑥) = - 1 \sqrt 1 - 𝑥 2 𝑑 𝑑 𝑥 (s e c - 1 𝑥) = 1 𝑥 \sqrt 𝑥 2 - 1 𝑑 𝑑 𝑥 (t a n - 1 𝑥) = 1 1 + 𝑥 2 𝑑 𝑑 𝑥 (c o t - 1 𝑥) = - 1 1 + 𝑥 2$

Hyperbolic

$R e m i n d e r : s i n h 𝑥 = 𝑒 𝑥 - 𝑒 - 𝑥 2 c o s h 𝑥 = 𝑒 𝑥 + 𝑒 - 𝑥 2 t a n h 𝑥 = s i n h 𝑥 c o s h 𝑥 c s c h 𝑥 = 1 s i n h 𝑥 s e c h 𝑥 = 1 c o s h 𝑥 c o t h 𝑥 = c o s h 𝑥 s i n h 𝑥$

$𝑑 𝑑 𝑥 (s i n h 𝑥) = c o s h 𝑥 𝑑 𝑑 𝑥 (c s c h 𝑥) = - c s c h 𝑥 c o t h 𝑥 𝑑 𝑑 𝑥 (c o s h 𝑥) = s i n h 𝑥 𝑑 𝑑 𝑥 (s e c h 𝑥) = - s e c h 𝑥 t a n h 𝑥 𝑑 𝑑 𝑥 (t a n h 𝑥) = s e c h 2 𝑥 𝑑 𝑑 𝑥 (c o t h 𝑥) = - c s c h 2 𝑥$

Tip: You can differentiate any function, for free,
using Wolfram WolframAlpha's Online Derivative Calculator.