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

Lösung

ableitung von

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

\frac{- x ^{2} + 10 x + 1}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x - 5) = 1

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

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

Vereinfache

\frac{1 \cdot ( x ^{2} + 1 ) - 2 x ( x - 5 )}{( x ^{2} + 1 ) ^{2}} : \frac{- x ^{2} + 10 x + 1}{( x ^{2} + 1 ) ^{2}}

= \frac{- x ^{2} + 10 x + 1}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (\frac{24}{x ^{4}})

\frac{d}{d x} (\frac{1}{5 + 3 x})

\frac{d}{d x} (5 x + \frac{7}{t})

\frac{d}{d x} (∣ sec (x) ∣)

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