Physics Exercises/Derivative Table

Current revision (unreviewed)

[edit] Some standard derivatives used in physics

$\frac{d}{d\theta}tan\theta=sec^2\theta$

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

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

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

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

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

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

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

$\frac{d}{dx}e^{kx}=ke^{kx}$

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

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

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

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

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

The following deal with the variable, $θ$ , and a function, $δ$ , of $θ$ , and are examples of the chain rule in action.

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

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

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

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