# 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

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

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