Engineering Tables/Properties of Derivatives

	Derivative	Conditions
1	${\frac {d}{dx}}c=0$
2	${\frac {d}{dx}}(cx)=c$
3 Elementary Power Rule	${\frac {d}{dx}}(x^{n})=nx^{n-1}$
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	${\frac {d}{dx}}\left({\frac {f}{g}}\right)={\frac {g{\frac {df}{dx}}-f{\frac {dg}{dx}}}{g^{2}}}$	$g\neq 0\,$
8 Chain Rule	${\frac {df}{dx}}={\frac {df}{dg}}\cdot {\frac {dg}{dx}}$
9	${\frac {d}{dx}}\left(f^{n}\right)=nf^{n-1}{\frac {df}{dx}}$
10 Reciprocal Rule	${\frac {d}{dx}}\left({\frac {1}{f}}\right)=-{\frac {1}{f^{2}}}{\frac {df}{dx}}$	$f\neq 0\,$
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	${\frac {df}{dx}}={\frac {1}{\frac {dx}{df}}}$	${\frac {dx}{df}}\neq 0\,$

Notes:	f, g, h are functions of x c, n are constants.

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