derivative of (20x/((x^2-4)^2))

Lösung

\frac{d}{d x} (\frac{20 x}{( x ^{2} - 4 ) ^{2}})

\frac{20 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

Schritte zur Lösung

\frac{d}{d x} (\frac{20 x}{( x ^{2} - 4 ) ^{2}})

Entferne die Konstante:

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

= 20 \frac{d}{d x} (\frac{x}{( x ^{2} - 4 ) ^{2}})

Wende die Quotientenregel an:

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

= 20 \cdot \frac{\frac{d x}{d x} ( x ^{2} - 4 ) ^{2} - \frac{d}{d x} ( ( x ^{2} - 4 ) ^{2} ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

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

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

= 20 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}}

Vereinfache

20 \cdot \frac{1 \cdot ( x ^{2} - 4 ) ^{2} - 4 x ( x ^{2} - 4 ) x}{( ( x ^{2} - 4 ) ^{2} ) ^{2}} : \frac{20 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

= \frac{20 ( - 3 x ^{2} - 4 )}{( x ^{2} - 4 ) ^{3}}

\int \frac{6}{x ^{2} - 4} d x

y^{^{'}} = b (1 - y) y

d er i v a t i v e 247 x - 19 x^{2}

\int {y (2 a x + b y)} d x

x \to - 3 lim (\frac{2}{x + 3})