d/(dt)((1-t^2)/(1+t^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

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

y^{^{'}} = 4 y^{2}

\frac{\partial}{\partial y} (600 - 4 x + 10 x^{2} y)

\int_{\frac{1}{2}}^{2} \frac{2}{x} - \frac{1}{2} x d x

\int \frac{4 - 32 x}{81 - 16 x ^{2}} d x