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

The answer to (\partial)/(\partial y)(5x^2y^3) is 15x^2y^2

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

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

15 x^{2} y^{2}

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 15 x^{2} y^{2}

\int e^{x} (e^{x} - 1) d x

4 x^{2} - 5 x + 2

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

\int \frac{- 8 x + 162}{x ^{2} + 9} d x

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

What is (\partial)/(\partial y)(5x^2y^3) ?
The answer to (\partial)/(\partial y)(5x^2y^3) is 15x^2y^2