derivative 1/(x(9+ln(x)))

Lösung

ableitung von

\frac{1}{x ( 9 + ln ( x ) )}

- \frac{ln ( x ) + 10}{x ^{2} ( 9 + ln ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{x ( 9 + ln ( x ) )})

Wende Exponentenregel an:

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

= \frac{d}{d x} ((x (9 + ln (x)))^{- 1})

Wende die Kettenregel an:

- \frac{1}{( x ( 9 + ln ( x ) ) ) ^{2}} \frac{d}{d x} (x (9 + ln (x)))

= - \frac{1}{( x ( 9 + ln ( x ) ) ) ^{2}} \frac{d}{d x} (x (9 + ln (x)))

\frac{d}{d x} (x (9 + ln (x))) = ln (x) + 10

= - \frac{1}{( x ( 9 + ln ( x ) ) ) ^{2}} (ln (x) + 10)

Vereinfache

- \frac{1}{( x ( 9 + ln ( x ) ) ) ^{2}} (ln (x) + 10) : - \frac{ln ( x ) + 10}{x ^{2} ( 9 + ln ( x ) ) ^{2}}

= - \frac{ln ( x ) + 10}{x ^{2} ( 9 + ln ( x ) ) ^{2}}

t a y l or ln (x), - 1

a re a y = (2 x - 7), (0, 7)

\frac{\partial}{\partial x} (ln (y^{x}))

\frac{d}{d x} (sin (- x))

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