derivative of (x^2/(5(1-x)))

Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 ( 1 - x )})

\frac{2 x - x ^{2}}{5 ( 1 - x ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2}}{5 ( 1 - x )})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (\frac{x ^{2}}{1 - x})

Wende die Quotientenregel an:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 1 - x ) - \frac{d}{d x} ( 1 - x ) x ^{2}}{( 1 - x ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

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

= \frac{1}{5} \cdot \frac{2 x ( 1 - x ) - ( - 1 ) x ^{2}}{( 1 - x ) ^{2}}

Vereinfache

\frac{1}{5} \cdot \frac{2 x ( 1 - x ) - ( - 1 ) x ^{2}}{( 1 - x ) ^{2}} : \frac{2 x - x ^{2}}{5 ( 1 - x ) ^{2}}

= \frac{2 x - x ^{2}}{5 ( 1 - x ) ^{2}}

t a y l or x^{0.5}

\frac{\partial}{\partial x} (2 x^{2} + 3 y - 20)

d er i v a t i v e (1 - x)^{3}

\frac{\partial}{\partial y} (- e^{x} sin (y) + \frac{1}{y})

x \to 0 lim (\frac{7 ^{x} - 5 ^{x}}{x})