Standardderivator

Derivator
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( c \right) = 0 \]	\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( cx \right) = c \]
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( cx^n \right) = ncx^{n-1} \]	\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \sin(x) \right) = \cos(x) \]
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \sin(x) \right) = \cos(x) \]	\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \cos(x) \right) = -\sin(x) \]
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left(\tan(x) \right)= \frac{1}{\cos^2(x)}\]	\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \arcsin(x) \right) =\frac{1}{\sqrt{1-x^2}} \]
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \arccos(x) \right) =-\frac{1}{\sqrt{1-x^2}} \]	\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \arctan(x) \right) =\frac{1}{1+x^2} \]
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \mathrm{e}^x \right) = \mathrm{e}^x \]	\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \mathrm{a}^x \right) =\ln(a)\mathrm{a}^x \]
\[ \frac{\mathrm{d}}{\mathrm{d}x}\left( \ln(x) \right) = \frac{1}{x} \]