derivative y=(2x+4)/(1-x)

Lösung

ableitung von

y = \frac{2 x + 4}{1 - x}

\frac{6}{( 1 - x ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{2 ( 1 - x ) - ( - 1 ) ( 2 x + 4 )}{( 1 - x ) ^{2}} : \frac{6}{( 1 - x ) ^{2}}

= \frac{6}{( 1 - x ) ^{2}}

\frac{d N}{d t} + N = Nt e^{t + 4}

\int_{0}^{1} x^{2} e^{x^{3}} d x

\frac{d y}{d x} = - 0.5 y + x

x \to 2 π lim (\frac{1}{sin ( x )})

ma c l a u r in sin (2 x)