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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

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

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

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

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

Vereinfache

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

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

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

x \to 0 lim (\frac{4}{3 + e ^{\frac{1}{x}}})

\frac{d}{d x} (sin (2 x + 3 y))

\frac{\partial}{\partial y} (ln (x^{2} + y))

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