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

The answer to (\partial)/(\partial y)(2x^2y+3xy^3) is 2x^2+9xy^2

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

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

2 x^{2} + 9 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial y} (3 x y^{3}) = 9 x y^{2}

= 2 x^{2} + 9 x y^{2}

\int_{0}^{8} x^{3} x^{2} + 64 d x

\frac{\partial}{\partial x} (e^{- 20})

\frac{d}{d x} (2 x^{6} - 9 x^{5} + 15 x^{4} - 10 x^{3} + 3 x - 1)

\frac{d}{d x} (\frac{x ^{2} + x - 12}{x - 4})

x \to 0 lim (\frac{2 x ^{2} + x}{x})

What is (\partial)/(\partial y)(2x^2y+3xy^3) ?
The answer to (\partial)/(\partial y)(2x^2y+3xy^3) is 2x^2+9xy^2