derivative of (3+sin(x)/(3x+cos(x)))

Lösung

\frac{d}{d x} (\frac{3 + sin ( x )}{3 x + cos ( x )})

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

Schritte zur Lösung

\frac{d}{d x} (\frac{3 + sin ( x )}{3 x + cos ( x )})

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (3 + sin (x)) = cos (x)

\frac{d}{d x} (3 x + cos (x)) = 3 - sin (x)

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

a re a y = e^{x}, y = e^{- 3 x}, x = - 2, x = 1

\frac{d}{d x} (e^{3 (x - 1)})

\int \frac{3}{2 + 3 x} d x

x \to - 3 lim (\frac{4 x}{x - 3})

\int sin (9 x) cos (2 x) d x