derivative of (sin(x)/(x+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

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

Vereinfache

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

l a pl a ce t r an s f or m 3 \cdot (5 e^{- 5.06 s}) + 3 \cdot (2.26 \cdot 5 e^{- 5.06 s})

\int \frac{( 9 4 - x ^{2} )}{2} d x

\frac{\partial}{\partial x} (sin (2 x + y))

\frac{d}{d x} (- (x - 3)^{2})

\int \frac{1}{x ^{2} + 2 x + 10} d x