What is (\partial)/(\partial y)(2x^2y+2y+5) ?

The answer to (\partial)/(\partial y)(2x^2y+2y+5) is 2x^2+2

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(\partial)/(\partial y)(2x^2y+2y+5)

\frac{\partial}{\partial y} (2 x^{2} y + 2 y + 5)

2 x^{2} + 2

Solution steps

\frac{\partial}{\partial y} (2 x^{2} y + 2 y + 5)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (2 x^{2} y) + \frac{\partial}{\partial y} (2 y) + \frac{\partial}{\partial y} (5)

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

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

\frac{\partial}{\partial y} (5) = 0

= 2 x^{2} + 2 + 0

Simplify

= 2 x^{2} + 2

x \to 0 lim (x + y)

y = \frac{3 + 5 x - 8 x}{x}

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

\frac{\partial}{\partial x} (x arctan (\frac{y}{z}))

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{15}})

What is (\partial)/(\partial y)(2x^2y+2y+5) ?
The answer to (\partial)/(\partial y)(2x^2y+2y+5) is 2x^2+2