de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative of ln((4x/(x+9)))

Lösung

\frac{d}{d x} (ln (\frac{4 x}{x + 9}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{4 x}{x + 9}))

Wende die Kettenregel an:

\frac{1}{\frac{4 x}{x + 9}} \frac{d}{d x} (\frac{4 x}{x + 9})

= \frac{1}{\frac{4 x}{x + 9}} \frac{d}{d x} (\frac{4 x}{x + 9})

\frac{d}{d x} (\frac{4 x}{x + 9}) = \frac{36}{( x + 9 ) ^{2}}

= \frac{1}{\frac{4 x}{x + 9}} \cdot \frac{36}{( x + 9 ) ^{2}}

Vereinfache

\frac{1}{\frac{4 x}{x + 9}} \cdot \frac{36}{( x + 9 ) ^{2}} : \frac{9}{x ( x + 9 )}

= \frac{9}{x ( x + 9 )}

Graph

Beliebte Beispiele

integral of 2/(x^2+1)

\int \frac{2}{x ^{2} + 1} d x

integral of 1/(x*sqrt(x^2-1))

\int \frac{1}{x \cdot x ^{2} - 1} d x

derivative of (4x/(x+3))

\frac{d}{d x} (\frac{4 x}{x + 3})

(dy)/(dx)=5y^2cos(x)

\frac{d y}{d x} = 5 y^{2} cos (x)

integral of 10xln(5x)

\int 10 x ln (5 x) d x