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

解答

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

8 z (4 x + 3 y)

求解步骤

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

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 + 3 y)^{2})

使用连锁律:

2 (4 x + 3 y) \frac{\partial}{\partial x} (4 x + 3 y)

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

\frac{\partial}{\partial x} (4 x + 3 y) = 4

= z \cdot 2 (4 x + 3 y) \cdot 4

化简

= 8 z (4 x + 3 y)

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