(\partial)/(\partial x)(y*sqrt(|x|))

解答

\frac{\partial}{\partial x} (y \cdot ∣ x ∣)

\frac{y x}{2 ∣ x ∣ ∣ x ∣}

求解步骤

\frac{\partial}{\partial x} (y ∣ x ∣)

将

y

视为常数

将常数提出:

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

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

使用连锁律:

\frac{1}{2 ∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

= \frac{1}{2 ∣ x ∣} \frac{\partial}{\partial x} (∣ x ∣)

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

= y \frac{1}{2 ∣ x ∣} \cdot \frac{x}{∣ x ∣}

化简

y \frac{1}{2 ∣ x ∣} \cdot \frac{x}{∣ x ∣} : \frac{y x}{2 ∣ x ∣ ∣ x ∣}

= \frac{y x}{2 ∣ x ∣ ∣ x ∣}

(x^{2} + 1) y^{^{'}} + 9 x (y - 1) = 0, y (0) = 2

\frac{d P}{d t} - a P = b

d x + e^{9 x} d y = 0

\frac{d}{d x} (- 2 x - 3 x^{3})

l a pl a ce t r an s f or m cos (\frac{1}{4} t)