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

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

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

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

x^{2} y^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

= x^{2} y^{3}

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