derivative of 1/(2sqrt(x)+1/(9x^{8/9)})

Lösung

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}})

- \frac{1}{4 x ^{\frac{3}{2}}} - \frac{8}{81 x ^{\frac{17}{9}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{2 x} + \frac{1}{9 x ^{\frac{8}{9}}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{2 x}) + \frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}}) = - \frac{8}{81 x ^{\frac{17}{9}}}

= - \frac{1}{4 x ^{\frac{3}{2}}} - \frac{8}{81 x ^{\frac{17}{9}}}

\int_{1}^{2} \frac{x - 1}{x} d x

\int e^{x} \cdot 2 x d x

d er i v a t i v e \frac{w}{w + \frac{c}{w}}

t an g e n t y = x^{2} - 6, at x = a

d er i v a t i v e \frac{x ^{2} - 4}{x - 3}