derivative of (10/(ln(x)))

Lösung

\frac{d}{d x} (\frac{10}{ln ( x )})

- \frac{10}{x ln ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{10}{ln ( x )})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (\frac{1}{ln ( x )})

Wende Exponentenregel an:

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

= 10 \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}

= 10 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Vereinfache

10 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{10}{x ln ^{2} ( x )}

= - \frac{10}{x ln ^{2} ( x )}

t^{2} \frac{d y}{d t} + y = 0, y (7) = - 4

\int sin (2 t) (cot (2 t) + 1) d t

\frac{d}{d x} (∣ x - 1 ∣^{3})

x \to 0 lim (∣ x - 1 ∣)

x \to 5 lim (2 x 5)