derivative y=(cos(x))/(1-sin(x))

解答

导数

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

\frac{1}{1 - sin ( x )}

求解步骤

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

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

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

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

化简

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

= \frac{1}{1 - sin ( x )}

d er i v a t i v e y = cos (sin (tan (9 x)))

\frac{\partial}{\partial x} (4 - x^{2} + x y - 2 y^{2})

t an g e n t x^{2} + y^{2} = 29, (- 5, 2)

\int_{0}^{1} \frac{x ^{2}}{1 + x ^{6}} d x

\int e^{- 2 l n (x)} d x