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

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

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

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

2 x y^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 2 x y^{3}

\int (x^{2} + 3 x - 2) d x

f (u) = u

\frac{d}{d x} (\frac{25 - x ^{2}}{8 x})

\int \frac{30}{1 - cos ( 6 x )} d x

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