derivative of (x^2-6x/(1+cos(x)))

Lösung

\frac{d}{d x} (\frac{x ^{2} - 6 x}{1 + cos ( x )})

\frac{( 2 x - 6 ) ( 1 + cos ( x ) ) + sin ( x ) ( x ^{2} - 6 x )}{( 1 + cos ( x ) ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{x ^{2} - 6 x}{1 + cos ( x )})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( x ^{2} - 6 x ) ( 1 + cos ( x ) ) - \frac{d}{d x} ( 1 + cos ( x ) ) ( x ^{2} - 6 x )}{( 1 + cos ( x ) ) ^{2}}

\frac{d}{d x} (x^{2} - 6 x) = 2 x - 6

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

= \frac{( 2 x - 6 ) ( 1 + cos ( x ) ) - ( - sin ( x ) ) ( x ^{2} - 6 x )}{( 1 + cos ( x ) ) ^{2}}

Vereinfache

= \frac{( 2 x - 6 ) ( 1 + cos ( x ) ) + sin ( x ) ( x ^{2} - 6 x )}{( 1 + cos ( x ) ) ^{2}}

\int \frac{1}{x ^{2} + 4 x + 25} d x

\int x 4 - x d x

\int_{0}^{1} 2 y^{2} d y

p a r i t y ln (e^{- x} + x e^{- x})

\frac{d}{d x} (\frac{5 x}{x - 3})