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

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

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

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

\int 8 cos (x) d x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} - 3 y = 2 x - 17

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

\int_{0}^{a} x sin^{2} (\frac{π}{a} x) d x

\frac{d x}{d t} = x (1 - x)

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