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Table of Derivatives


A table of derivatives can be a handy tool, so I've included some of the more common ones here.


(1)\(\frac{d}{dx}(c)=0\)

(2)\(\frac{d}{dx}(x^n)\)\(=nx^{n-1}\)

(3)\(\frac{d}{dx}(u\pm v)\) \(=\frac{du}{dx}\pm\frac{dv}{dx}\)

(4)\(\frac{d}{dx}(uv)\) \(=u\frac{du}{dx}+\frac{dv}{dx}\)

(5)\(\frac{d}{dx}(cv)\) \(=c\frac{dv}{dx}\)

(6)\(\frac{d}{dx}(\frac{u}{v})\) \(=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}\)

(7)\(\frac{d}{dx}F(x)\) \(=\frac{d}{dx}f(u)\cdot\frac{d}{dx}g(x)\)

(8)\(\frac{d}{dx}([u(x)^n])\) \(=n[u(x)]^{n-1}\cdot\frac{d}{dx}(u(x))\)

(9)\(\frac{d}{dx}sin\,u\) \(=cos\,u\frac{du}{dx}\)

(10)\(\frac{d}{dx}cos\,u\) \(=-sin\,u\frac{du}{dx}\)

(11)\(\frac{d}{dx}tan\,u\) \(=sec^2\,u\frac{du}{dx}\)

(12)\(\frac{d}{dx}cot\,u\) \(=-csc^2\,u\frac{du}{dx}\)

(13)\(\frac{d}{dx}sec\,u\) \(=sec\,u\,tan\,u\frac{du}{dx}\)

(14)\(\frac{d}{dx}csc\,u\) \(=-csc\,u\,cot\,u\frac{du}{dx}\)

(15)\(\frac{d}{dx}sin^{-1}\,u\) \(=\frac{u′}{\sqrt{1-u^2}}\)

(16)\(\frac{d}{dx}cos^{-1}\,u\) \(=\frac{-u′}{\sqrt{1-u^2}}\)

(17)\(\frac{d}{dx}tan^{-1}\,u\) \(=\frac{u′}{1+u^2}\)

(18)\(\frac{d}{dx}cot^{-1}\,u\) \(=\frac{-u′}{1+u^2}\)

(19)\(\frac{d}{dx}sec^{-1}\,u\) \(=\frac{u′}{u\sqrt{u^2-1}}\)

(20)\(\frac{d}{dx}csc^{-1}\,u\) \(=\frac{-u′}{u\sqrt{u^2-1}}\)

(21)\(\frac{d}{dx}log_au\) \(=\frac{u′}{u}log_aε\)

(22)\(\frac{d}{dx}ln\,u\) \(=\frac{u′}{u}\)

(23)\(\frac{d}{dx}a^u\) \(=a^u\cdot ln\,a\)

(24)\(\frac{d}{dx}ε^u\) \(=ε^u\cdot u′\)

(25)\(\frac{d}{dx}\) \(=\)