Differentialkvotienter for simple funktioner

Ting der er gode at huske.

f(x)=ax+b
LaTex: f'(x) = a
f(x)=k
LaTex: f'(x) = 0
f(x)=ax²
LaTex: f'(x) = 2\cdot a\cdot x
f(x)=x^(0,5)
LaTex: f'(x) = \frac{1}{2\cdot\sqrt{x}}
f(x)=1/x
LaTex: f'(x) = \frac{-1}{x^2}
f(x)=ax^n
LaTex: f'(x) = anx^{(n-1)}
f(x)=a/(x^n)
LaTex: f'(x) = \frac{-n\cdot a}{x^{n+1}}

LaTeX tabel

LaTex: \begin{tabular}{| c |c |} \hline f(x) & f'(x)\\\hline a\cdot x + b & a\\\hline k & 0\\\hline a\cdot a^2 & 2\cdot a \cdot x\\\hline \sqrt{x} & \frac{1}{2\cdot \sqrt{x}}\\\hline \frac{1}{x} & \frac{-1}{x^2}\\\hline a\cdot x^n & a\cdot n\cdot x^{n-1}\\\hline \frac{a}{x^n} & \frac{-n\cdot a}{x^{n+1}}\\ \hline \end{tabular}

Se evt.

Hentet fra "http://jopsen.dk/wiki/Differentialkvotienter_for_simple_funktioner/"