(\partial)/(\partial x)(x/(sqrt(1+x^2)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Vereinfache

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

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

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

t an g e n t 4 x^{2} - x^{3}

\int_{- \infty}^{0} \frac{1}{5 - 10 x} d x

\int \frac{π}{2}

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