derivative of (x+1/x ^2)

Lösung

\frac{d}{d x} ((x + \frac{1}{x})^{2})

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

Schritte zur Lösung

\frac{d}{d x} ((x + \frac{1}{x})^{2})

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (2) = 0

\frac{d}{d x} (\frac{1}{x ^{2}}) = - \frac{2}{x ^{3}}

= 2 x + 0 - \frac{2}{x ^{3}}

Vereinfache

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

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

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

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

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

ma c l a u r in 5 cos (π x)