derivative (c^2-x^2)/(c^2+x^2)

Lösung

ableitung von

\frac{c ^{2} - x ^{2}}{c ^{2} + x ^{2}}

- \frac{4 c ^{2} x}{( c ^{2} + x ^{2} ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 x ) ( c ^{2} + x ^{2} ) - 2 x ( c ^{2} - x ^{2} )}{( c ^{2} + x ^{2} ) ^{2}} : - \frac{4 c ^{2} x}{( c ^{2} + x ^{2} ) ^{2}}

= - \frac{4 c ^{2} x}{( c ^{2} + x ^{2} ) ^{2}}

n = 0 \sum \infty n + 1

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

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

x \to 0 lim (\frac{x - 1}{x ^{2} - 1})

d er i v a t i v e (x^{2} + 1) (x + 5 + \frac{1}{x})