(\partial)/(\partial x)((z)(4x^2y+3y-5))

解答

\frac{\partial}{\partial x} ((z) (4 x^{2} y + 3 y - 5))

8 z x y

求解步骤

\frac{\partial}{\partial x} ((z) (4 x^{2} y + 3 y - 5))

将

z, y

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (4 x^{2} y + 3 y - 5)

使用微分加减法定则:

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

= z (\frac{\partial}{\partial x} (4 x^{2} y) + \frac{\partial}{\partial x} (3 y) - \frac{\partial}{\partial x} (5))

\frac{\partial}{\partial x} (4 x^{2} y) = 8 y x

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

\frac{\partial}{\partial x} (5) = 0

= z (8 y x + 0 - 0)

化简

= 8 z x y

e x p an d \frac{( - 4 x ^{2} + 7 x + 2 ) ( x + 1 )}{2}

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

e x p an d \frac{14 v ( 6 v - 5 )}{3}

e x p an d \frac{( 11 x ^{4} + 2 ) ^{5}}{2}

e x p an d (x_{0} + e x_{1} + x_{2} e^{2})^{3}