derivative of (11/(ln(x)))

Lösung

\frac{d}{d x} (\frac{11}{ln ( x )})

- \frac{11}{x ln ^{2} ( x )}

Schritte zur Lösung

\frac{d}{d x} (\frac{11}{ln ( x )})

Entferne die Konstante:

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

= 11 \frac{d}{d x} (\frac{1}{ln ( x )})

Wende Exponentenregel an:

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

= 11 \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}

= 11 (- \frac{1}{( ln ( x ) ) ^{2}} \cdot \frac{1}{x})

Vereinfache

11 (- \frac{1}{ln ^{2} ( x )} \cdot \frac{1}{x}) : - \frac{11}{x ln ^{2} ( x )}

= - \frac{11}{x ln ^{2} ( x )}

x \frac{d y}{d x} + y = sin (x)

t an g e n t f (x) = 2 x^{2} - 6 x + 6, at x = 7

\frac{\partial}{\partial x} (x \cdot y \cdot ln (x^{2} + y^{2}))

d er i v a t i v e ln (1 + e^{x})

t an g e n t \frac{5 x}{x + 4}