d/(dt)((tsin(t))/(1+t))

Lösung

\frac{d}{d t} (\frac{t sin ( t )}{1 + t})

\frac{t ^{2} cos ( t ) + t cos ( t ) + sin ( t )}{( 1 + t ) ^{2}}

Schritte zur Lösung

\frac{d}{d t} (\frac{t sin ( t )}{1 + t})

Wende die Quotientenregel an:

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

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

\frac{d}{d t} (t sin (t)) = sin (t) + t cos (t)

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

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

Vereinfache

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

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

\int 0.1 x^{2} d x

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