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Beliebt Rechnen >

derivative f(x)= 1/(sqrt(x+1))

Lösung

ableitung von

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

Lösung

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

Schritte zur Lösung

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

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

limit as x approaches infinity of y^{-x}

x \to \infty lim (y^{- x})

limit as x approaches 2 of 5

x \to 2 lim (5)

fläche e^{-x},0,0,ln(3)

a re a e^{- x}, 0, 0, ln (3)

(dy)/(dt)=6y+2t-4,y(0)=3

\frac{d y}{d t} = 6 y + 2 t - 4, y (0) = 3

limit as x approaches 4 of (x^2)/(x-4)

x \to 4 lim (\frac{x ^{2}}{x - 4})