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

The answer to (\partial)/(\partial y)(e^{xy^2}) is e^{xy^2}*2xy

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

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

e^{x y^{2}} \cdot 2 x y

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= e^{x y^{2}} \cdot 2 x y

What is (\partial)/(\partial y)(e^{xy^2}) ?
The answer to (\partial)/(\partial y)(e^{xy^2}) is e^{xy^2}*2xy