derivative y= 1/(ln(x))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

\frac{d}{d 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 )}

\int \frac{2 x}{( x - 1 ) ^{5}} d x

f (t) = ln (t)

\int 2^{s i n (x)} cos (x) d x

0.145 \cdot \frac{d v}{d t} = (0.145 \cdot 9.81) - (0.043 \cdot v)

(x, y) \to (0, 0) lim (∣ x + y ∣)