derivative (sin(x))/(2+cos(x))

解答

导数

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

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

求解步骤

\frac{d}{d x} (\frac{sin ( x )}{2 + cos ( x )})

使用微分除法定则:

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

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

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

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

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

化简

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

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

t a y l or sin (5 x), x = 0

d er i v a t i v e \frac{1}{ln ( x + 1 )}

\frac{\partial}{\partial y} (5 x + y)

\frac{d}{d a} (sin^{4} (a) + cos^{4} (a))

\int \frac{sec ( x ) tan ( x )}{- 5 + sec ( x )} d x