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

The answer to (\partial)/(\partial y)(2xy^2+y) is 4xy+1

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

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

4 x y + 1

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (2 x y^{2}) = 4 x y

\frac{\partial}{\partial y} (y) = 1

= 4 x y + 1

f (x) = (\frac{x}{x ^{2} + 1})^{2}

\frac{d y}{d x} + y = x e^{- x} + 1

n = 0 \sum \infty \frac{1}{n ( n + 2 )}

x \to 5 lim (x^{2} - 25)

\frac{d}{d x} (x (x^{2} + 1)^{2})

What is (\partial)/(\partial y)(2xy^2+y) ?
The answer to (\partial)/(\partial y)(2xy^2+y) is 4xy+1