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

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

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

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

x e^{x y} x

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x e^{x y} x

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