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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int_{0}^{2} x \cdot 3^{x} d x

\int cot^{3} (x) \cdot csc^{2} (x) d x

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\int x^{3} 2 x + 1 d x

\frac{d}{d x} (sin (x) + cos (x) + tan (x))