(\partial)/(\partial x)(x^{1/4}*y^{1/2})

解答

\frac{\partial}{\partial x} (x^{\frac{1}{4}} \cdot y^{\frac{1}{2}})

\frac{y ^{\frac{1}{2}}}{4 x ^{\frac{3}{4}}}

求解步骤

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{1}{2}})

将

y

视为常数

将常数提出:

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

= y^{\frac{1}{2}} \frac{\partial}{\partial x} (x^{\frac{1}{4}})

使用幂法则:

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

= y^{\frac{1}{2}} \frac{1}{4} x^{\frac{1}{4} - 1}

化简

y^{\frac{1}{2}} \frac{1}{4} x^{\frac{1}{4} - 1} : \frac{y ^{\frac{1}{2}}}{4 x ^{\frac{3}{4}}}

= \frac{y ^{\frac{1}{2}}}{4 x ^{\frac{3}{4}}}

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