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

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

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

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

e^{x^{y}} x^{y} ln (x)

Solution steps

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

Treat

x

as a constant

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^{y} ln (x)

= e^{x^{y}} x^{y} ln (x)

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