(\partial)/(\partial y)(({g}(y,x))(x+y))

解答

\frac{\partial}{\partial y} ((g (y, x)) (x + y))

\frac{\partial}{\partial y} (g (y, x)) (x + y) + 1 \cdot g (y, x)

求解步骤

\frac{\partial}{\partial y} ((g (y, x)) (x + y))

将

x

视为常数

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = g (y, x), g = x + y

= \frac{\partial}{\partial y} (g (y, x)) (x + y) + \frac{\partial}{\partial y} (x + y) g (y, x)

\frac{\partial}{\partial y} (x + y) = 1

= \frac{\partial}{\partial y} (g (y, x)) (x + y) + 1 \cdot g (y, x)

e x p an d \frac{d}{d x} ((x - 2) e^{x}) + x

e x p an d (x - 1 + \frac{1}{x})^{2}

e x p an d (x - 6 + 5) (x - 6 - 5) (x - 4)

e x p an d \frac{61 ( y ^{2} - 14 y + 49 )}{12}

e x p an d \frac{2 ( 2 a - 1 )}{3 ( 10 a ^{2} - 5 )}