# Differentiation Formula

## Basic Rule

 Constant Rule \frac{d(c)}{dx}=0;    c = constant Power Rule \frac{d(x)}{dx}=1 \frac{d(cx)}{dx}=c×1 \frac{d(x^n)}{dx}=nx^{n-1} \frac{d(cx^n)}{dx}=c×nx^{n-1} Exponential Function \frac{d(e^x)}{dx}=e^x \frac{d(e^{mx})}{dx}=me^{mx} \frac{d(a^x)}{dx}=a^xloga \frac{d(a^{mx})}{dx}=ma^{mx}loga Logarithmic Function \frac{d(logx)}{dx}={1\over x} \frac{d(logmx)}{dx}={1\over x} Product Rule Quotient Rule \frac{duv}{dx}=u \frac{dv}{dx}+v \frac{du}{dx} \frac{d{u\over v}}{dx}={v \frac{du}{dx}-u \frac{dv}{dx}\over v^2}

## Trigonometric Functions

 \frac{d(sinx)}{dx}=cosx \frac{d(sinmx)}{dx}=mcosmx \frac{d(cosx)}{dx}=-sinx \frac{d(cosmx)}{dx}=-msinmx \frac{d(tanx)}{dx}=sec^2x \frac{d(tanmx)}{dx}=sec^2mx \frac{d(secx)}{dx}=secxtanx \frac{d(secmx)}{dx}=msecmxtanmx \frac{d(cotx)}{dx}=-cosec^2x \frac{d(cotmx)}{dx}=-mcosec^2mx \frac{d(cosecx)}{dx}=-cosecxcotx \frac{d(cosecmx)}{dx}=-mcosecxcotmx

## Inverse Trigonometric Functions

 \frac{d(sin^{-1}x)}{dx}={1\over \sqrt{1-x^2}} \frac{d(cos^{-1}x)}{dx}=-{1\over \sqrt{1-x^2}} \frac{d(tan^{-1}x)}{dx}={1\over 1+x^2} \frac{d(cot^{-1}x)}{dx}=-{1\over 1+x^2} \frac{d(sec^{-1}x)}{dx}={1\over |x|\sqrt{1-x^2}} \frac{d(cosec^{-1}x)}{dx}=-{1\over |x|\sqrt{1-x^2}}
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