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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)$$\frac{d}{dx}$$ $$=$$