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

The answer to (\partial)/(\partial y)(e^{2xy^2}+3x) is 4e^{2xy^2}xy

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

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

4 e^{2 x y^{2}} x y

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial y} (3 x) = 0

= e^{2 x y^{2}} \cdot 4 x y + 0

Simplify

= 4 e^{2 x y^{2}} x y

What is (\partial)/(\partial y)(e^{2xy^2}+3x) ?
The answer to (\partial)/(\partial y)(e^{2xy^2}+3x) is 4e^{2xy^2}xy