(\partial)/(\partial x)(1/(ln(x/2)))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

t an g e n t y = e^{5 x}, at x = \frac{1}{5} ln (3)

(- 2 sin (x))^{^{'}}

d er i v a t i v e x^{3} + \frac{1}{x ^{3}}

t a y l or ln (x + 2)

\int ln (x) ln (x) d x