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Beliebt Rechnen >

derivative of (1-2x/(4+x))

Lösung

\frac{d}{d x} (\frac{1 - 2 x}{4 + x})

Lösung

- \frac{9}{( 4 + x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1 - 2 x}{4 + x})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 1 - 2 x ) ( 4 + x ) - \frac{d}{d x} ( 4 + x ) ( 1 - 2 x )}{( 4 + x ) ^{2}}

\frac{d}{d x} (1 - 2 x) = - 2

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

sum from n=0 to infinity of 4(2/3)^{2n}

n = 0 \sum \infty 4 (\frac{2}{3})^{2 n}

integral of x^{-7/4}

\int x^{- \frac{7}{4}} d x

derivative f(x)= x/(2(x^2+7)^{3/4)}

d er i v a t i v e f (x) = \frac{x}{2 ( x ^{2} + 7 ) ^{\frac{3}{4}}}

derivative of sin(5x+2)

\frac{d}{d x} (sin (5 x + 2))

derivative f(x)=(x+1)/x

d er i v a t i v e f (x) = \frac{x + 1}{x}