derivative of 1/(ln(x+x))

Lösung

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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

a re a x^{2} 1, 0, 1

in v erse l a pl a ce \frac{4 s ^{3}}{( s + 5 ) ^{9}}

x \to 2 lim (5 x - 6)

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