derivative of ((xcos(x+pi))/(x-pi))

解答

\frac{d}{d x} (\frac{( x cos ( x ) + π )}{x - π})

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

求解步骤

\frac{d}{d x} (\frac{( x cos ( x ) + π )}{x - π})

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

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

\frac{d}{d x} (x - π) = 1

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

化简

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

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

d er i v a t i v e x^{- 0.5}

\frac{d ^{2}}{d x ^{2}} (e^{x})

x \to 2 lim (4 x^{2} - 2 x)

\int x \cdot 2^{- x} d x

\frac{\partial}{\partial x} (5 e^{7 x} sin (7 y))