Table of derivatives

For any constant a:
:a'=0
For any real number r:
:(x^r)'=rx^{r-1} (Power rule)
For any real-valued differentiable functions f(x) and g(x):
*a\,f'(x)=a\,f'(x)
*(f(x)+g(x))'=f'(x)+g'(x) 
*\left(cf\right)' = c\left(f'\right) (Constant rule)
*\left(-f\right)' = -\left(f'\right)
*\left(fg\right)' = f'g+fg' (Product rule)
*\left( \frac 1 g \right)' = -\frac {g'} {g^2}
*\left( \frac f g \right)' = \frac {f'g-fg'}{g^2} (Quotient rule)
*\left(f\circ g\right)' = \left(f'\circ g\right)g' (Chain rule)
Trigonometric functions:
*(\sin(x))' = \cos(x)
*(\cos(x))' = -\sin(x)
*(\tan(x))' = \sec^2(x)
*(\csc(x))' = -\csc(x) \cot(x)
*(\sec(x))' = \sec(x) \tan(x)
*(\cot(x))' = -\csc^2(x)
*(\arcsin(x))' = \frac{1}{\sqrt{1-x^2}}
*(\arccos(x))' = -\frac{1}{\sqrt{1-x^2}}
*(\arctan(x))' = \frac{1}{1+x^2}
*(\arcsec(x))' = \frac{1}{|x|\sqrt{x^2-1}}
*(\arccsc(x))' = -\frac{1}{|x|\sqrt{x^2-1}}
*(\arccot(x))' = -\frac{1}{x^2+1}
Logarithmic and exponential functions:
*(e^x)'=e^x
*(a^x)'=a^x \ln(a)
*(\ln x)'=\frac{1}{x}
*(\log_{a}x)'=\frac{1}{x \ln(a)}
==See also==
*Table of integrals
*Derivative
Category:Tables
Category:Mathematical operations