d/(dt)((cos(t)+sin(t))/(-sin(t)+cos(t)))

解答

\frac{d}{d t} (\frac{cos ( t ) + sin ( t )}{- sin ( t ) + cos ( t )})

\frac{2}{1 - sin ( 2 t )}

求解步骤

\frac{d}{d t} (\frac{cos ( t ) + sin ( t )}{- sin ( t ) + cos ( t )})

使用微分除法定则:

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

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

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

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

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

化简

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

= \frac{2}{1 - sin ( 2 t )}

\int \frac{26}{x + x x} d x

x \to 0 lim ((x + 2)^{2})

t an g e n t x^{4} - 25 x^{2} + 144

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

\frac{d}{d x} (4 7 x)