Engineering Tables/Properties of Derivatives

	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	$\frac{d}{dx}(f\pm g\pm h\pm \cdots )=\frac{df}{dx}\pm \frac{dg}{dx}\pm \frac{dh}{dx}\pm \cdots$
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	$\frac{d}{dx}\left(f^g\right)=\frac{d}{dx}\left(e^{g\ln f}\right)=f^g(\frac{g}{f}\cdot \frac{df}{dx}+\frac{dg}{dx}\ln f)$	$f>0$
12 Logarithm Rule	$\frac{df}{dx}=f\frac{d}{dx}(\ln f)$	$f>0$
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.
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