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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Multipliziere aus

cos (x) (1 + sin (x)) - cos (x) sin (x) : cos (x)

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

\int_{1}^{\infty} (\frac{1}{x ^{3}}) d x

l a pl a ce t r an s f or m 4 t^{2} cos (2 t) + 5 t e^{- 7 t}

\frac{d}{d x} (4 x^{9} + 2 x^{5})

d er i v a t i v e f (x) = \frac{c ^{5} - x ^{5}}{c ^{5} + c ^{5}}

f^{^{'}} (t) - f (t) = 6 t