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

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

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

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

2 x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x y + 0

Simplify

= 2 x y

x \to 0 lim (x^{6} cos (\frac{9}{x}))

x \to - \infty lim (5 x^{3})

\frac{\partial}{\partial x} ((x^{0.5} + y^{0.5})^{2})

\int 7 u^{7} u^{8} + 7 d u

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

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