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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

\frac{d}{d v} (\frac{u}{v})

\int_{0}^{1} - 2 (x^{2} + 1) e^{- x} d x

f (x) = arcsec (2 x)

5 t - 3

\frac{\partial}{\partial x} ((x + y)^{8})

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