derivative (1-cos(x))/(1+x-e^x)

解答

导数

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

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

求解步骤

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

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

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

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

\frac{d}{d x} (5 x + 5)

d er i v a t i v e y (θ) = arctan (cos (θ))

\int x (2 - x)^{2} d x

\int_{0}^{5} x 1 + x d x

d er i v a t i v e e^{x^{3} + 2 x}