derivative (x^2)/(4(2-x))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int 9 y^{- 2} d y

d er i v a t i v e f (x) = x^{2} - 25

x \to 0 lim (\frac{sin ( 6 x )}{sin ( 9 x )})

t y^{^{'}} + (t + 1) y = t, y (ln (7)) = 1

\frac{d}{d x} (5 x^{3} + 2 ln (x))