(\partial)/(\partial x)(1/({f)(x)})

Lösung

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

- \frac{\frac{\partial}{\partial x} ( f ( x ) )}{f ( x ) ^{2}}

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

Vereinfache

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

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

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

\frac{d}{d x} (ln (x^{2} + 4))

\frac{\partial}{\partial x} (e^{- 2 x} sin (y))

n = 1 \sum \infty \frac{n ^{4}}{4 ^{n}}

a re a x, \frac{1}{x ^{2}}, [0, 1]