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

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

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

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

2 y + 3 x y^{2}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y + 3 x y^{2}

\frac{d}{d x} ((x - 4)^{3} + 3 x (x - 4)^{2})

\int (2 sin (4 x) - 8 cos (3 x)) d x

\int_{0}^{1} x e^{- 5 x} d x

\frac{d}{d x} ((x + 4)^{3} (x - 3)^{6})

x \to 4 lim (2 - x)

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