derivative (2t)/(t^2+1)

Lösung

ableitung von

\frac{2 t}{t ^{2} + 1}

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

\frac{d t}{d t} = 1

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

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

Vereinfache

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

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

\frac{d}{d x} ((5 x^{2} - 3) \cdot (x^{2} + x + 4))

\frac{d}{d x} (e^{x} (12 x^{2} - 24 x + 24))

\frac{d}{d x} (e^{x t a n (x)})

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

a re a y^{2} = x - 1, 1, 3