(\partial)/(\partial x)(zln|x|)

解答

\frac{\partial}{\partial x} (z ln ∣ x ∣)

\frac{z}{x}

求解步骤

\frac{\partial}{\partial x} (z ln ∣ x ∣)

将

z

视为常数

将常数提出:

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

= z \frac{\partial}{\partial x} (ln ∣ x ∣)

使用连锁律:

\frac{1}{∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

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

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

= z \frac{1}{∣ x ∣} \cdot \frac{x}{∣ x ∣}

化简

z \frac{1}{∣ x ∣} \cdot \frac{x}{∣ x ∣} : \frac{z}{x}

= \frac{z}{x}