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

The answer to (\partial)/(\partial x)(x^{2/3}*y^{1/2}) is (2y^{1/2})/(3x^{1/3)}

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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}}}

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

- \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)

What is (\partial)/(\partial x)(x^{2/3}*y^{1/2}) ?
The answer to (\partial)/(\partial x)(x^{2/3}*y^{1/2}) is (2y^{1/2})/(3x^{1/3)}