(\partial)/(\partial x)(1/(x+1))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

d er i v a t i v e 2 (x) + 1

a re a - 7 x^{2} + 63, - x^{2} + 9

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

d er i v a t i v e f (x) = x^{\frac{1}{5}}

s im pl i f y \frac{x + 1}{x ^{2} + 1}