(\partial)/(\partial x)(In|x-y|)

解答

\frac{\partial}{\partial x} (I n ∣ x - y ∣)

\frac{n I ( x - y )}{∣ x - y ∣}

求解步骤

\frac{\partial}{\partial x} (I n ∣ x - y ∣)

将

n, I, y

视为常数

将常数提出:

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

= I n \frac{\partial}{\partial x} (∣ x - y ∣)

使用连锁律:

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

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

\frac{\partial}{\partial x} (x - y) = 1

= I n \frac{x - y}{∣ ( x - y ) ∣} \cdot 1

化简

I n \frac{x - y}{∣ x - y ∣} \cdot 1 : \frac{n I ( x - y )}{∣ x - y ∣}

= \frac{n I ( x - y )}{∣ x - y ∣}

x \to 2 lim (e^{\frac{3}{( 2 - x )}})

y^{^{''}} - y^{^{'}} - 12 y = 2 e^{3 x}

\frac{\partial}{\partial v} (u (v) (v)^{2} e^{- v})

x \to - 7 lim (\frac{x + 7}{∣ x + 7 ∣})

\int_{1}^{e} ln (10 x) d x