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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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