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

Lösung

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

\frac{cos ( x ) ( x + 1 ) - 2 sin ( x )}{( x + 1 ) ^{3}}

Schritte zur Lösung

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

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

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

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

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

Vereinfache

\frac{cos ( x ) ( x + 1 ) ^{2} - 2 ( x + 1 ) sin ( x )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{cos ( x ) ( x + 1 ) - 2 sin ( x )}{( x + 1 ) ^{3}}

= \frac{cos ( x ) ( x + 1 ) - 2 sin ( x )}{( x + 1 ) ^{3}}

\frac{\partial}{\partial x} (x^{2} + 8)

\frac{d}{d x} (x^{x^{x^{x^{x}}}})

\int \frac{x ^{3} - 1}{x - 1} d x

\int (\frac{sin ( x )}{cos ^{2} ( x )}) d x

n = 2 \sum \infty \frac{8}{4 ^{2 n}}