derivative y=((x+1)^2)/(sqrt(x)+1)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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