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

Lösung

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

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

Schritte zur Lösung

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

Vereinfache

\frac{- x}{1 + x ^{2}} : - \frac{x}{1 + x ^{2}}

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d 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}}

a re a y = x^{3} - x^{2}, y = 0

\frac{\partial}{\partial x} (3 x^{2} y^{4} + 1)

\int \frac{1}{x 9 x ^{2} - 4} d x

k = 1 \sum \infty k^{3} \cdot e^{- k^{2}}

\frac{\partial}{\partial x} (4 x^{6} + x y^{3} + 2 y^{4})