(\partial)/(\partial x)((3x^2+5x+1)(y+4))

解答

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1) (y + 4))

(y + 4) (6 x + 5)

求解步骤

\frac{\partial}{\partial x} ((3 x^{2} + 5 x + 1) (y + 4))

将

y

视为常数

将常数提出:

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

= (y + 4) \frac{\partial}{\partial x} (3 x^{2} + 5 x + 1)

使用微分加减法定则:

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

= (y + 4) (\frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (5 x) + \frac{\partial}{\partial x} (1))

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

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

\frac{\partial}{\partial x} (1) = 0

= (y + 4) (6 x + 5 + 0)

化简

= (y + 4) (6 x + 5)

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