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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

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

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

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

(x + 2)^{2} y^{^{'}} + 8 y = 5 - 4 x y

x \to 4 lim (x^{2} - 5 x + 7 x^{3})

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

\int \frac{( u ^{2} ) ^{22}}{1 + ( u ^{2} ) ^{22}} d (u^{2})^{2}