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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

d er i v a t i v e y = - 8

\frac{\partial}{\partial y} (\frac{m}{y} - 625 \frac{y}{x})

d er i v a t i v e f (x) = x^{3} (x^{2} + 4)^{- 2}

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

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