(\partial)/(\partial x)(1/(ln(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{\partial}{\partial x} (e^{x^{2} + y^{2} + z^{2}})

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

\frac{\partial}{\partial y} (ln (x - 5 y))

a re a x^{2} + 4 x + 3, y = - 2, - 2 < x < 0

a re a x = y + 2, x = y^{2}