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

d er i v a t i v e y = \frac{x ^{2}}{5 - 8 x}

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

x \to 0 lim (x^{3} \cdot sin (\frac{1}{x}))

x \to 0 lim ((1 - 2 x)^{\frac{5}{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