derivative of 2/x+sqrt(x)

Lösung

\frac{d}{d x} (\frac{2}{x} + x)

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

Schritte zur Lösung

\frac{d}{d x} (\frac{2}{x} + x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{2}{x}) + \frac{d}{d x} (x)

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

\frac{d}{d x} (x) = \frac{1}{2 x}

= - \frac{2}{x ^{2}} + \frac{1}{2 x}

Vereinfache

- \frac{2}{x ^{2}} + \frac{1}{2 x} : \frac{- 4 + x ^{\frac{3}{2}}}{2 x ^{\frac{3}{2}} x}

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

\frac{\partial}{\partial v} (\frac{1}{u ^{2} + v ^{2}})

\int \frac{7 + 6 x}{1 + x ^{2}} d x

x \to 3 lim (2 x - 5)

x \to \frac{π}{x} lim (x cos (x))

x \to - 2 lim (3 x + 2)