(\partial)/(\partial x)(x^{2/3}*y^{1/2})

解答

\frac{\partial}{\partial x} (x^{\frac{2}{3}} \cdot y^{\frac{1}{2}})

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

求解步骤

\frac{\partial}{\partial x} (x^{\frac{2}{3}} 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{2}{3}})

使用幂法则:

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

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

化简

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

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

d er i v a t i v e \frac{x ^{2} - 1}{x - 1}

in v erse l a pl a ce - \frac{6}{( s - 2 ) ^{2}}

\frac{d}{d x} (e^{x y} + ln (\frac{x}{y}))

\frac{d y}{d x} = 4 + y - 4 x + 2

x \to 0 lim (a x)