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

Lösung

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

\frac{2 ( - 5 x ^{2} - 3 )}{( x ^{2} - 3 ) ^{4}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((x^{2} - 3)^{3}) = 6 x (x^{2} - 3)^{2}

= 2 \cdot \frac{1 \cdot ( x ^{2} - 3 ) ^{3} - 6 x ( x ^{2} - 3 ) ^{2} x}{( ( x ^{2} - 3 ) ^{3} ) ^{2}}

Vereinfache

2 \cdot \frac{1 \cdot ( x ^{2} - 3 ) ^{3} - 6 x ( x ^{2} - 3 ) ^{2} x}{( ( x ^{2} - 3 ) ^{3} ) ^{2}} : \frac{2 ( - 5 x ^{2} - 3 )}{( x ^{2} - 3 ) ^{4}}

= \frac{2 ( - 5 x ^{2} - 3 )}{( x ^{2} - 3 ) ^{4}}

3 y^{^{''}} - 16 y^{^{'}} + 5 y = 0, y (0) = - 3, y^{^{'}} (0) = 4

d er i v a t i v e \frac{1}{( x - 4 ) ^{2}}

d er i v a t i v e f (x) = (3 x^{2} + 6 x)^{3}

\int 0.06 x^{2} - 4.4 x + 60 d x

x \to 0 lim (2 x tan (3 x))