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

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

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

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

3 x y^{2}

Solution steps

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

\frac{\partial}{\partial y} (x^{2}) = 0

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

= 0 + 3 x y^{2}

Simplify

= 3 x y^{2}

5 \frac{d y}{d t} + y = 20 t

\int e^{5 - 2 x} d x

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

\frac{d y}{d x} (x) = y

\frac{\partial}{\partial x} ((x - a)^{2})

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