(\partial)/(\partial x)(ln(x+8y+7z))

解答

\frac{\partial}{\partial x} (ln (x + 8 y + 7 z))

\frac{1}{x + 8 y + 7 z}

求解步骤

\frac{\partial}{\partial x} (ln (x + 8 y + 7 z))

将

y, z

视为常数

使用连锁律:

\frac{1}{x + 8 y + 7 z} \frac{\partial}{\partial x} (x + 8 y + 7 z)

= \frac{1}{x + 8 y + 7 z} \frac{\partial}{\partial x} (x + 8 y + 7 z)

\frac{\partial}{\partial x} (x + 8 y + 7 z) = 1

= \frac{1}{x + 8 y + 7 z} \cdot 1

化简

= \frac{1}{x + 8 y + 7 z}