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

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

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

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

3 x^{2} y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 3 x^{2} y^{2}

\frac{4 x ^{3} + 2 x + 5}{x}

x \to 0 lim (\frac{5 ^{x} - 3 ^{x}}{x})

\int (- x^{5} + 6 e^{- 2 x}) d x

(x + y) y^{^{'}} = x - y

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

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