(\partial)/(\partial x)(2y^2sqrt(x))

解答

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

\frac{y ^{2}}{x}

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用根式运算法则:

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

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

使用幂法则:

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

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

化简

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

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

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