derivative of sqrt(x)+1/x

Lösung

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

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Vereinfache

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

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

\int 2 x + 5 d x

t an g e n t f (x) = - 2 x^{4}, at x = 3

\frac{d}{d r} (- arctan (r) + 2 arccot (r) - ln (r))

\int 19 d x

\frac{\partial}{\partial x} (2 x + 5 y)