What is (\partial)/(\partial x)(5x^2y^3) ?

The answer to (\partial)/(\partial x)(5x^2y^3) is 10xy^3

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(\partial)/(\partial x)(5x^2y^3)

\frac{\partial}{\partial x} (5 x^{2} y^{3})

10 x y^{3}

Solution steps

\frac{\partial}{\partial x} (5 x^{2} y^{3})

Treat

y

as a constant

Take the constant out:

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

= 5 y^{3} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

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

= 5 y^{3} \cdot 2 x^{2 - 1}

Simplify

= 10 x y^{3}

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What is (\partial)/(\partial x)(5x^2y^3) ?
The answer to (\partial)/(\partial x)(5x^2y^3) is 10xy^3