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

Lösung

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

- \frac{4 x}{( 1 + x ^{2} ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{( - 2 x ) ( 1 + x ^{2} ) - 2 x ( 1 - x ^{2} )}{( 1 + x ^{2} ) ^{2}} : - \frac{4 x}{( 1 + x ^{2} ) ^{2}}

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

\frac{\partial}{\partial x} (\frac{m \cdot x \cdot T}{A})

x \to 1 + lim (7 ∣ x + 1 ∣ - 4)

\int_{0}^{3} 9 + x^{2} d x

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

\int_{- L}^{L} x^{2} d x