derivative of 4/(sqrt(x)+2/x+x/2)

Lösung

\frac{d}{d x} (\frac{4}{x} + \frac{2}{x} + \frac{x}{2})

\frac{1}{2} + \frac{- 2 x ^{2} - 2 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{4}{x} + \frac{2}{x} + \frac{x}{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (\frac{2}{x}) + \frac{d}{d x} (\frac{x}{2})

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

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

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

= - \frac{2}{x ^{\frac{3}{2}}} - \frac{2}{x ^{2}} + \frac{1}{2}

Ziehe Brüche zusammen

- \frac{2}{x ^{\frac{3}{2}}} - \frac{2}{x ^{2}} : \frac{- 2 x ^{2} - 2 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

= \frac{1}{2} + \frac{- 2 x ^{2} - 2 x ^{\frac{3}{2}}}{x ^{\frac{7}{2}}}

\int \frac{( x - 1 ) ( x + 1 )}{x} d x

x \to π lim (15)

x \to 3 lim (5 x^{3} - 2 x^{2} + x - 7)

\int 2 x^{2} 3 3 x^{3} + 4 d x

d er i v a t i v e - 0.6 t^{3} + 7.2 t^{2} + 61