Math cheatsheet

Calculus

Product Rule	\(\left( uv \right)' = u'v + uv'\)
Quotent Rule	\(\left( \frac{u}{v} \right)' = \frac{vu' - uv'}{v^2}\)
Chain Rule	\(\frac{d}{dt}\left[ u\left( v(t) \right)\right] = u'(v(t))v'(t)\)
Integration by Parts	\(\int u dv = uv - \int vdu\)

Useful derivatives

\(\frac{d}{dt}t^n\)	\(=\)	\(nt^{n-1}\)
\(\frac{d}{dt}e^t\)	\(=\)	\(e^{t}\)
\(\frac{d}{dt}ln(t)\)	\(=\)	\(\frac{1}{t}\), \(t > 0\)
\(\frac{d}{dt}ln(u(t))\)	\(=\)	\(\frac{u'(t)}{u(t)}\)
\(\frac{d}{dt}sin(t)\)	\(=\)	\(cos(t)\)
\(\frac{d}{dt}cos(t)\)	\(=\)	\(-sin(t)\)

Trig Identities

\(\tan \theta\)	\(=\)	\(\frac{\cos\theta}{\sin\theta}\)
\(\sin^2 \theta + \cos^2 \theta\)	\(=\)	\(1\)
\(\sin \frac{\theta}{2}\)	\(=\)	\(\pm \sqrt{\frac{1 - \cos\theta}{2}}\)
\(\cos \frac{\theta}{2}\)	\(=\)	\(\pm \sqrt{\frac{1 + \cos\theta}{2}}\)
\(\tan \frac{\theta}{2}\)	\(=\)	\(\frac{1 - \cos\theta}{\sin\theta}\)

Quadratic formula

\[\begin{align} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \\ \end{align}\]