(\partial)/(\partial x)(-15(3x+y)^4)

解答

\frac{\partial}{\partial x} (- 15 (3 x + y)^{4})

- 180 (3 x + y)^{3}

求解步骤

\frac{\partial}{\partial x} (- 15 (3 x + y)^{4})

将

y

视为常数

将常数提出:

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

= - 15 \frac{\partial}{\partial x} ((3 x + y)^{4})

使用连锁律:

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

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

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

= - 15 \cdot 4 (3 x + y)^{3} \cdot 3

化简

= - 180 (3 x + y)^{3}