(\partial)/(\partial y)(xye^y+e^ysin(x))

解答

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

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

求解步骤

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

将

x

视为常数

使用微分加减法定则:

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

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

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

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

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

\frac{\partial}{\partial x} (16 - x^{2} - y^{2})

a re a y = e^{- 2 x} + 1, y = 0, x = 0, x = 3

\frac{\partial}{\partial t} (3 e^{s i n (x + 4 c t)})

f (x) = x^{6 x}

y^{^{'}} = \frac{( 4 x ^{3} + y ^{3} )}{x y ^{2}}