derivative of sqrt(x)-2/x

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

d er i v a t i v e x^{5}

t a y l or \frac{x}{1 + 2 x ^{2}}

\int \frac{7 x ^{2} - 4 x + 4}{( x + 1 ) ( x ^{2} - x + 1 )} d x

d er i v a t i v e (3 + csc (2 t))^{- 6}

t an g e n t f (x) = - 2 - cos (x), at x = - \frac{π}{4}