(\partial)/(\partial x)((y)(x^2+6xy+y^3))

解答

\frac{\partial}{\partial x} ((y) (x^{2} + 6 x y + y^{3}))

y (6 y + 2 x)

求解步骤

\frac{\partial}{\partial x} ((y) (x^{2} + 6 x y + y^{3}))

将

y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= y \frac{\partial}{\partial x} (x^{2} + 6 x y + y^{3})

使用微分加减法定则:

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

= y (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (y^{3}))

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (y^{3}) = 0

= y (2 x + 6 y + 0)

化简

= y (6 y + 2 x)

s im pl i f y (x + \frac{1}{4}) (x + \frac{3}{4})

so l v e f or j, m = 4 i - 7 j - k^{0}

e x p an d k e^{8 (k + 1)}

e x p an d (15 + j^{37.89}) x - (j^{37}, 89) y

e x p an d \frac{1}{s e ^{3 (s - 1)}}