derivative of x/(y^2+1)

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d x}{d x} = 1

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

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

Vereinfache

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

\frac{d}{d x} (lo g_{e} (2))

\frac{d ^{2}}{d x ^{2}} (x e^{- \frac{x ^{2}}{2}})

\int x x - 8 d x

t an g e n t 3 x^{2} + x y + 3 y^{2} = 7, (1, 1)

t an g e n t \frac{sin ( t )}{2 + 2 cos ( t )}