derivative of ((x-1^4)/((x^2+2x)^5))

Lösung

\frac{d}{d x} (\frac{( x - 1 ) ^{4}}{( x ^{2} + 2 x ) ^{5}})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{( x - 1 ) ^{4}}{( x ^{2} + 2 x ) ^{5}})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( ( x - 1 ) ^{4} ) ( x ^{2} + 2 x ) ^{5} - \frac{d}{d x} ( ( x ^{2} + 2 x ) ^{5} ) ( x - 1 ) ^{4}}{( ( x ^{2} + 2 x ) ^{5} ) ^{2}}

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

\frac{d}{d x} ((x^{2} + 2 x)^{5}) = 5 (x^{2} + 2 x)^{4} (2 x + 2)

= \frac{4 ( x - 1 ) ^{3} ( x ^{2} + 2 x ) ^{5} - 5 ( x ^{2} + 2 x ) ^{4} ( 2 x + 2 ) ( x - 1 ) ^{4}}{( ( x ^{2} + 2 x ) ^{5} ) ^{2}}

Vereinfache

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

= \frac{2 ( x - 1 ) ^{3} ( - 3 x ^{2} + 4 x + 5 )}{( x ^{2} + 2 x ) ^{6}}

\frac{d}{d y} (e^{x} (x - y)^{2})

\frac{\partial}{\partial x} (cos^{3} (x))

\frac{\partial}{\partial y} (\frac{4 x}{3 y ^{2} + 1})

x \to 2 lim (3 + x)

\frac{d}{d x} (\frac{e ^{x}}{7 x ^{2}})