(\partial)/(\partial y)(ye^{xy}sin(y))

解答

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

e^{y x} sin (y) + y (e^{y x} x sin (y) + e^{y x} cos (y))

求解步骤

\frac{\partial}{\partial y} (y e^{x y} sin (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 = y, g = e^{x y} sin (y)

= \frac{\partial}{\partial y} (y) e^{x y} sin (y) + \frac{\partial}{\partial y} (e^{x y} sin (y)) y

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

\frac{\partial}{\partial y} (e^{x y} sin (y)) = e^{x y} x sin (y) + cos (y) e^{x y}

= 1 \cdot e^{x y} sin (y) + (e^{x y} x sin (y) + cos (y) e^{x y}) y

化简

= e^{y x} sin (y) + y (e^{y x} x sin (y) + e^{y x} cos (y))

x \to 2 - lim (3 x)

5 x^{^{''}} + 50 x - 10 = 0

\frac{\partial}{\partial y} ((2 x + 3 y)^{7})

\frac{d}{d u} (ln (u cos (v)))

\frac{d y}{d x} = x y, y (0) = 2