derivative (x^2)/((x^2-1)^4)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} ((x^{2} - 1)^{4}) = 8 x (x^{2} - 1)^{3}

= \frac{2 x ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x ^{2}}{( ( x ^{2} - 1 ) ^{4} ) ^{2}}

Vereinfache

\frac{2 x ( x ^{2} - 1 ) ^{4} - 8 x ( x ^{2} - 1 ) ^{3} x ^{2}}{( ( x ^{2} - 1 ) ^{4} ) ^{2}} : \frac{2 x ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{5}}

= \frac{2 x ( - 3 x ^{2} - 1 )}{( x ^{2} - 1 ) ^{5}}

\frac{\partial}{\partial y} (x^{2} e^{y})

s l o p e in t erce pt (7) (- 1.6)

x^{2} y^{^{'}} + 2 x y = 11 cos^{2} (x)

d er i v a t i v e y = lo g_{5} (7 x + 1)

\frac{d}{d x} (\frac{4 x ^{3}}{3})