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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to 3 - lim (\frac{1}{∣ x - 3 ∣})

\int_{0}^{9} x d x

\frac{d}{d x} f (x) = (4 x^{(4)} + 6)^{(3)}

s l o p e g (x) = 5 x^{2} - x + 7

\frac{d}{d x} ((8 + 7 x)^{4})