What is a summary of Differentiation Rules?

Aug 4, 2014

Power rule:
if $f \left(x\right) = {x}^{n}$ then $f ' \left(x\right) = n {x}^{n - 1}$

Sum rule:
if $f \left(x\right) = g \left(x\right) + h \left(x\right)$ then $f ' \left(x\right) = g ' \left(x\right) + h ' \left(x\right)$

Product rule:
if $f \left(x\right) = g \left(x\right) h \left(x\right)$ then $f ' \left(x\right) = g ' \left(x\right) h \left(x\right) + g \left(x\right) h ' \left(x\right)$

Quotient rule:
if $f \left(x\right) = g \frac{x}{h \left(x\right)}$ then $f ' \left(x\right) = \frac{g ' \left(x\right) h \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2$

Chain rule:
if $f \left(x\right) = h \left(g \left(x\right)\right)$ then $f ' \left(x\right) = h ' \left(g \left(x\right)\right) g ' \left(x\right)$
Or:
$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$