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

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

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

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

x^{2} + 3 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{\partial}{\partial x} (cos (x) cos (y))

\frac{d x}{d t} = \frac{457.8 - 7 x}{2180}

(1 - e^{x^{3}})^{5}

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

y = \frac{x ^{2} - 1}{x ^{2} + x + 1}, (1, 0)

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