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} \cdot 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 (x + a) (x + b) d x

y^{^{''}} + 20 y^{^{'}} + 500 = 12

\int \frac{1}{x - 1 + 1 + x} d x

y^{^{'}} = 2 + y - 2 x + 3

\frac{d}{d x} (\frac{2}{( x + 3 ) ^{3}})

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