derivative of 8/(sqrt(x)-4/x)

Lösung

\frac{d}{d x} (\frac{8}{x} - \frac{4}{x})

\frac{- 4 x ^{2} + 4 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{8}{x} - \frac{4}{x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{8}{x}) - \frac{d}{d x} (\frac{4}{x})

\frac{d}{d x} (\frac{8}{x}) = - \frac{4}{x ^{\frac{3}{2}}}

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

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

Vereinfache

- \frac{4}{x ^{\frac{3}{2}}} - (- \frac{4}{x ^{2}}) : \frac{- 4 x ^{2} + 4 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

= \frac{- 4 x ^{2} + 4 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

\frac{\partial}{\partial y} (yz - ln (x + z))

x \to 2 lim (3 x^{2} + 1)

d er i v a t i v e y = 300 (1.056)^{x}

\frac{\partial}{\partial x} (3 x^{2} + 2 x y^{2} + 1)

n = 1 \sum \infty \frac{5}{π ^{2}}