de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

derivative (-200ln(f/(40)))/((f+20))

Lösung

ableitung von

\frac{- 200 ln ( \frac{f}{40} )}{( f + 20 )}

Lösung

- \frac{200 ( f + 20 - f ln ( \frac{f}{40} ) )}{f ( f + 20 ) ^{2}}

Schritte zur Lösung

\frac{d}{df} \frac{- 200 ln ( \frac{f}{40} )}{f + 20}

Vereinfache

\frac{- 200 ln ( \frac{f}{40} )}{f + 20} : - \frac{200 ln ( \frac{f}{40} )}{f + 20}

= \frac{d}{df} - \frac{200 ln ( \frac{f}{40} )}{f + 20}

Entferne die Konstante:

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

= - 200 \frac{d}{df} \frac{ln ( \frac{f}{40} )}{f + 20}

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 200 \cdot \frac{\frac{d}{df} ( ln ( \frac{f}{40} ) ) ( f + 20 ) - \frac{d}{df} ( f + 20 ) ln ( \frac{f}{40} )}{( f + 20 ) ^{2}}

\frac{d}{df} (ln (\frac{f}{40})) = \frac{1}{f}

\frac{d}{df} (f + 20) = 1

= - 200 \cdot \frac{\frac{1}{f} ( f + 20 ) - 1 \cdot ln ( \frac{f}{40} )}{( f + 20 ) ^{2}}

Vereinfache

- 200 \cdot \frac{\frac{1}{f} ( f + 20 ) - 1 \cdot ln ( \frac{f}{40} )}{( f + 20 ) ^{2}} : - \frac{200 ( f + 20 - f ln ( \frac{f}{40} ) )}{f ( f + 20 ) ^{2}}

= - \frac{200 ( f + 20 - f ln ( \frac{f}{40} ) )}{f ( f + 20 ) ^{2}}

Graph

Beliebte Beispiele

derivative of y/(1+x^2)

\frac{d}{d x} (\frac{y}{1 + x ^{2}})

integral from 1 to infinity of 1/(n^2)

\int_{1}^{\infty} \frac{1}{n ^{2}}

fläche x,2-x,0

a re a x, 2 - x, 0

derivative e^{-t^2}

d er i v a t i v e e^{- t^{2}}

limit as x approaches 0 of (2x-2)/x

x \to 0 lim (\frac{2 x - 2}{x})