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

Lösung

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

\frac{- x ^{2} + 8 x + 1}{( x ^{2} + 1 ) ^{2}}

Schritte zur Lösung

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

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

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

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

Vereinfache

\frac{1 \cdot ( x ^{2} + 1 ) - 2 x ( x - 4 )}{( x ^{2} + 1 ) ^{2}} : \frac{- x ^{2} + 8 x + 1}{( x ^{2} + 1 ) ^{2}}

= \frac{- x ^{2} + 8 x + 1}{( x ^{2} + 1 ) ^{2}}

\frac{d}{d x} (I n (3 x))

\frac{\partial}{\partial y} (x^{0.5} y^{0.5})

\frac{d}{d x} (cos (3 x^{2} - 2 x))

\int \frac{x ^{3}}{5 x ^{4} - 1} d x

\int (3 x + 4)^{3} d x