Last modified on 30 July 2010, at 17:32

Physics Exercises/Derivative Table

Some standard derivatives used in physicsEdit

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

\frac{d}{d\theta}\cot\theta=-\csc^2\theta

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

\frac{d}{d\theta}\csc\theta=-\csc\theta \cot\theta

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

\frac{d}{d\theta}\sin k\theta=k\cos k\theta

\frac{d}{d\theta}\cos k\theta=-k\sin k\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, \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