What is (\partial)/(\partial y)(2x^2y^3) ?

The answer to (\partial)/(\partial y)(2x^2y^3) is 6x^2y^2

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(\partial)/(\partial y)(2x^2y^3)

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

6 x^{2} y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 6 x^{2} y^{2}

What is (\partial)/(\partial y)(2x^2y^3) ?
The answer to (\partial)/(\partial y)(2x^2y^3) is 6x^2y^2