derivative of (sin(x-1)/(cos(x)+1))

解答

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

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

求解步骤

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

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

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

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

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

化简

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

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

\frac{d}{d x} (arctan (\frac{x ^{2}}{y}))

t an g e n t 11 x^{\frac{1}{2}} + x^{\frac{3}{2}}

\int_{1}^{e} ln (5 x) d x

d er i v a t i v e x + 1