derivative of (1-x/((x+1)^3))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (1 - x) = - 1

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

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

Vereinfache

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

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

\frac{d}{d x} (\frac{3 x}{1 + 2 x})

\int (cos (x) + \frac{1}{4} x) d x

\int sin^{23} (x) d x

x \to - 4 + lim (5 x + 20 - 8)

n = 0 \sum \infty - 1^{n}