What is (\partial)/(\partial x)(4x^{2/3}y^{1/3}) ?

The answer to (\partial)/(\partial x)(4x^{2/3}y^{1/3}) is (8y^{1/3})/(3x^{1/3)}

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(\partial)/(\partial x)(4x^{2/3}y^{1/3})

\frac{\partial}{\partial x} (4 x^{\frac{2}{3}} y^{\frac{1}{3}})

\frac{8 y ^{\frac{1}{3}}}{3 x ^{\frac{1}{3}}}

Solution steps

\frac{\partial}{\partial x} (4 x^{\frac{2}{3}} y^{\frac{1}{3}})

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

4 y^{\frac{1}{3}} \frac{2}{3} x^{\frac{2}{3} - 1} : \frac{8 y ^{\frac{1}{3}}}{3 x ^{\frac{1}{3}}}

= \frac{8 y ^{\frac{1}{3}}}{3 x ^{\frac{1}{3}}}

t (e^{t} + e^{2 t})^{2}

\frac{d}{d x} (0.5 e^{\frac{x}{3}} - sin (x))

\int_{0}^{4} x - 2 x d x

\int - x x - 1 d x

x \to \infty lim (sin (arctan (x)))

What is (\partial)/(\partial x)(4x^{2/3}y^{1/3}) ?
The answer to (\partial)/(\partial x)(4x^{2/3}y^{1/3}) is (8y^{1/3})/(3x^{1/3)}