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}=msec^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}=-mcosecmxcotmx |
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}} |
