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

Lösung

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

\frac{16 x}{( 4 - x ^{2} ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

2 \cdot \frac{2 x ( 4 - x ^{2} ) - ( - 2 x ) x ^{2}}{( 4 - x ^{2} ) ^{2}} : \frac{16 x}{( 4 - x ^{2} ) ^{2}}

= \frac{16 x}{( 4 - x ^{2} ) ^{2}}

y^{^{'''}} - 2 y^{^{''}} - 4 y^{^{'}} + 8 y = 6 x e^{2 x}

\int \frac{13}{( x - 7 ) ( x + 6 )} d x

f (x) = tan (x^{2})

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

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{- x}, y (0) = 4, y^{^{'}} (0) = - 1