derivative of (x-x^2/(2-3x+x^2))

Lösung

\frac{d}{d x} (\frac{x - x ^{2}}{2 - 3 x + x ^{2}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{x - x ^{2}}{2 - 3 x + x ^{2}})

Vereinfache

\frac{x - x ^{2}}{2 - 3 x + x ^{2}} : - \frac{x}{x - 2}

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

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

\int_{0}^{l n (6)} e^{x} - e^{- 3 x} d x

d er i v a t i v e y = \frac{4 x}{9 - tan ( x )}

d er i v a t i v e arctan (x)

\int_{0}^{1} (x 2 - x^{2}) d x

t an g e n t y = \frac{x}{( 1 + x ^{2} ) , at ( 3 , 0.3 )}