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Beliebt Rechnen >

derivative of 1+1/(sqrt(x))

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{1}{2 x ^{\frac{3}{2}}}

Vereinfache

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

Graph

Beliebte Beispiele

xy^'=y+8x^2sin(x),y(pi)=0

x y^{^{'}} = y + 8 x^{2} sin (x), y (π) = 0

x^2(dy)/(dx)+2xy-y^3=0

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

derivative of (sqrt(10)/(x^7))

\frac{d}{d x} (\frac{10}{x ^{7}})

limit as x approaches 0-of 1/(3x)

x \to 0 - lim (\frac{1}{3 x})

fläche y=sqrt(3x),x=3,y=1

a re a y = 3 x, x = 3, y = 1