(\partial)/(\partial p)((p+q)/(p+r))

解答

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

\frac{- q + r}{( p + r ) ^{2}}

求解步骤

\frac{\partial}{\partial p} (\frac{p + q}{p + r})

将

q, r

视为常数

使用微分除法定则:

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

= \frac{\frac{\partial}{\partial p} ( p + q ) ( p + r ) - \frac{\partial}{\partial p} ( p + r ) ( p + q )}{( p + r ) ^{2}}

\frac{\partial}{\partial p} (p + q) = 1

\frac{\partial}{\partial p} (p + r) = 1

= \frac{1 \cdot ( p + r ) - 1 \cdot ( p + q )}{( p + r ) ^{2}}

化简

\frac{1 \cdot ( p + r ) - 1 \cdot ( p + q )}{( p + r ) ^{2}} : \frac{- q + r}{( p + r ) ^{2}}

= \frac{- q + r}{( p + r ) ^{2}}

d er i v a t i v e \frac{1}{d + k e ^{d}}

\frac{d ^{2}}{d x ^{2}} y + 36 y = 0

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

\frac{d}{d x} (\frac{3 x - 5}{x ^{2} + 7})

\frac{d}{d x} (- 12 e^{- 2 x})