Regneregler

Denne artikel om handler regne regler for differential kvotienter, og andre relaterede ting.

Plus minus

LaTex: \begin{eqnarray} f(x) &,& g(x)\\ f'(x) &,& g'(x)\\ h(x)&=& f(x)\pm g(x)\\ h'(x) &=& f'(x)\pm g'(x)\\ \end{eqnarray}

Eksempel
LaTex: \begin{eqnarray} f(x) &=& 5\cdot x^2\\ g(x) &=& \frac{1}{x}\\ f'(x) &=& 2\cdot 5\cdot x_0\\ g'(x) &=& \frac{-1}{x_0^2}\\ h(x) &=& f(x) + g(x) = 5\cdot x^2 +\frac{1}{x}\\ h'(x) &=& f'(x) + g'(x) = 2\cdot 5\cdot x_0+\frac{-1}{x_0^2}\\ \end{eqnarray}

Multiplikation og division

Se evt. side 47 i Matematik 2A bogen.

LaTex: \begin{eqnarray} f(x) &,& g(x)\\ f'(x) &,& g'(x)\\ \left(f\cdot g\right)(x) &=& f(x)\cdot g(x)\\ \left(f\cdot g\right)'(x) &=& f'(x)\cdot g(x)+f(x)\cdot g'(x)\\ \left(\frac{f}{g}\right)(x) &=& \frac{f(x)}{ g(x)}\\ \left(\frac{f}{g}\right)'(x) &=& \frac{f'(x)\cdot g(x)-f(x)\cdot g'(x)}{g(x)^2}\\ \end{eqnarray}

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