(\partial)/(\partial y)(xsqrt(y))

解答

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

\frac{x}{2 y}

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用根式运算法则:

a = a^{\frac{1}{2}}

= x \frac{\partial}{\partial y} (y^{\frac{1}{2}})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x \frac{1}{2} y^{\frac{1}{2} - 1}

化简

x \frac{1}{2} y^{\frac{1}{2} - 1} : \frac{x}{2 y}

= \frac{x}{2 y}