derivative of 2/(sqrt(x+1))

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende Exponentenregel an:

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

= 2 \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

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

Vereinfache

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

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

\int \frac{2 x}{1 - x ^{4}} d x

s l o p e (- 2.9) (- 1.7)

\frac{d}{d x} (sin^{x} (x))

t an g e n t f (x) = 5 x - 9 x^{2}, at x = 1

\frac{d}{d x} (- 8 cos (x))