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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

Graph

Beliebte Beispiele

derivative (x-3)(x+2)(x+3)

d er i v a t i v e (x - 3) (x + 2) (x + 3)

integral of (sqrt(1+x^2))/x

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

derivative 45+22sin((2pi)/(52)(t-10))

d er i v a t i v e 45 + 22 sin (\frac{2 π}{52} (t - 10))

12y^{''}-5y^'-3y=0

12 y^{^{''}} - 5 y^{^{'}} - 3 y = 0

integral of 1/(25e^{-5x)+e^{5x}}

\int \frac{1}{25 e ^{- 5 x} + e ^{5 x}} d x