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

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

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

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

2 y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (5 x e^{x^{2}}) = 0

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

= 0 + 2 y

Simplify

= 2 y

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

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

arctan (\frac{1}{x})

\frac{\partial}{\partial v} (sin (v))

\frac{1}{x + 4}, 0

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