derivative (2x)/((x^3-6)^2)

Lösung

ableitung von

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

\frac{2 ( - 5 x ^{3} - 6 )}{( x ^{3} - 6 ) ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

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

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

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

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

Vereinfache

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

= \frac{2 ( - 5 x ^{3} - 6 )}{( x ^{3} - 6 ) ^{3}}

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

d er i v a t i v e \frac{1}{3} x^{3} + 8 x^{2} + 63 x + 7

y^{^{''}} x + (\frac{2}{x} - \frac{2 x}{1 + x ^{2}}) \cdot y^{^{'}} = 0

\frac{d}{d x} (2 cos (x) - 4 sin (x))

\int 2 arcsin (2 x) d x