(\partial)/(\partial x)((F(x,y))/(V(x,y))x-(F(x,y))/(V(x,y))y-ky^n)

解答

\frac{\partial}{\partial x} (\frac{F ( x , y )}{V ( x , y )} x - \frac{F ( x , y )}{V ( x , y )} y - k y^{n})

(\frac{\frac{\partial}{\partial x} ( F ( x , y ) ) V ( x , y ) - \frac{\partial}{\partial x} ( V ( x , y ) ) F ( x , y )}{V ( x , y ) ^{2}} x + 1 \cdot \frac{F ( x , y )}{V ( x , y )}) - y \frac{\frac{\partial}{\partial x} ( F ( x , y ) ) V ( x , y ) - \frac{\partial}{\partial x} ( V ( x , y ) ) F ( x , y )}{V ( x , y ) ^{2}} - 0

求解步骤

\frac{\partial}{\partial x} (\frac{F ( x , y )}{V ( x , y )} x - \frac{F ( x , y )}{V ( x , y )} y - k y^{n})

将

k, n, y

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (\frac{F ( x , y )}{V ( x , y )} x) - \frac{\partial}{\partial x} (\frac{F ( x , y )}{V ( x , y )} y) - \frac{\partial}{\partial x} (k y^{n})

\frac{\partial}{\partial x} (\frac{F ( x , y )}{V ( x , y )} x) = \frac{\frac{\partial}{\partial x} ( F ( x , y ) ) V ( x , y ) - \frac{\partial}{\partial x} ( V ( x , y ) ) F ( x , y )}{V ( x , y ) ^{2}} x + 1 \cdot \frac{F ( x , y )}{V ( x , y )}

\frac{\partial}{\partial x} (\frac{F ( x , y )}{V ( x , y )} y) = y \frac{\frac{\partial}{\partial x} ( F ( x , y ) ) V ( x , y ) - \frac{\partial}{\partial x} ( V ( x , y ) ) F ( x , y )}{V ( x , y ) ^{2}}

\frac{\partial}{\partial x} (k y^{n}) = 0

= (\frac{\frac{\partial}{\partial x} ( F ( x , y ) ) V ( x , y ) - \frac{\partial}{\partial x} ( V ( x , y ) ) F ( x , y )}{V ( x , y ) ^{2}} x + 1 \cdot \frac{F ( x , y )}{V ( x , y )}) - y \frac{\frac{\partial}{\partial x} ( F ( x , y ) ) V ( x , y ) - \frac{\partial}{\partial x} ( V ( x , y ) ) F ( x , y )}{V ( x , y ) ^{2}} - 0

\frac{d}{d x} (7^{5 x})

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

\int_{- 3}^{3} (x + 2) d x

\int_{- 1}^{1} x sin (nπ x) d x

\frac{\partial}{\partial t} (e^{- π t})