Engineering Tables/Properties of Derivatives

Current revision (unreviewed)

	Derivative	Conditions
1	$\frac{d}{dx}c = 0$
2	$\frac{d}{dx} (cx) = c$
3 Elementary Power Rule	$\frac{d}{dx} (x^n) = n x^{n-1}$
4 Sum Rule	$\frac{d}{dx} \left( f \pm g \pm h \pm \cdots \right) = \frac{df}{dx} \pm \frac{dg}{dx} \pm \frac{dh}{dx} \pm \cdots$
5 Constant Multiple Rule	$\frac{d}{dx} (cf) = c \frac{df}{dx}$
6 Product Rule	$\frac{d}{dx} (fg) = f \frac{dg}{dx} + g \frac{df}{dx}$
6 Product Rule (Extended)	$\frac{d}{dx} (fgh) = fg \frac{dh}{dx} + fh \frac{dg}{dx} + gh \frac{df}{dx}$
7 Quotient Rule	$\frac{d}{dx} \left( \frac{f}{g} \right) = \frac{g \frac{df}{dx} - f \frac{dg}{dx}}{g^2}$	$g \ne 0\,$
8 Chain Rule	$\frac{df}{dx} = \frac{df}{dg} \cdot \frac{dg}{dx}$
9	$\frac{d}{dx} \left( f^n \right) = n f^{n-1} \frac{df}{dx}$
10 Reciprocal Rule	$\frac{d}{dx}\left( \frac{1}{f} \right) = -\frac{1}{f^2}\frac{df}{dx}$	$f \ne 0\,$
11 Functional Power Rule	$\frac{d}{dx} \left( f^g \right) = \frac{d}{dx} \left( e^{g \ln f} \right) = f^g \left(\frac{g}{f} \cdot \frac{df}{dx}+ \frac{dg}{dx} \ln f \right)$	$f > 0\,$
12 Logarithm Rule	$\frac{df}{dx} = f \frac{d}{dx} \left( \ln f \right)$	$f > 0\,$
13 Inverse Function Rule	$\frac{df}{dx} = \frac{1}{\frac{dx}{df}}$	$\frac{dx}{df} \ne 0\,$

Notes:	f, g, h are functions of x c, n are constants.
This transcluded page: view • talk • edit