Physics Exercises/Derivative Table

Some standard derivatives used in physics

$\frac{d}{d\theta }tan\theta =se{c}^2\theta$

$\frac{d}{d\theta }cot\theta =-cose{c}^2\theta$

$\frac{d}{d\theta }sec\theta =sec\theta tan\theta$

$\frac{d}{d\theta }cosec\theta =-cosec\theta cot\theta$

$\frac{d}{d\theta }{e}^x=e^x$

$\frac{d}{d\theta }sink\theta =kcosk\theta$

$\frac{d}{d\theta }cosk\theta =-ksinl\theta$

$\frac{d}{d\theta }\sqrt{\theta }=\frac{1}{2\sqrt{\theta }}$

$\frac{d}{d\theta }{e}^{kx}=k{e}^{kx}$

$\frac{d}{d\theta }ln\theta =\frac{1}{\theta }$

$\frac{d}{d\theta }si{n}^{-1}\theta =\frac{1}{\sqrt{1-{\theta }^2}}$

$\frac{d}{d\theta }co{s}^{-1}\theta =\frac{-1}{\sqrt{1-{\theta }^2}}$

$\frac{d}{d\theta }ta{n}^{-1}\theta =\frac{1}{1+{\theta }^2}$

$\frac{d}{d\theta }{e}^{i\theta }=i{e}^{i\theta }$, where $i=\sqrt{-1}$

The following deal with the variable, $\theta$, and a function, $\delta$, of $\theta$, and are examples of the chain rule in action.

$\frac{d}{d\theta }sin\delta =(cos\delta )\frac{d}{d\theta }\delta$

$\frac{d}{d\theta }{\delta }^4=(4{\delta }^3)\frac{d}{d\theta }\delta$

$\frac{d}{d\theta }{\theta }^3\delta =3{\theta }^2\delta +({\theta }^3)\frac{d}{d\theta }\delta$

$\frac{d}{d\theta }{\theta }^2{\delta }^2=2\theta {\delta }^2+(2{\theta }^2\delta )\frac{d}{d\theta }\delta$

--Afrowildo 21:54, 26 January 2007 (UTC)