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

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

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

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

e^{e^{x y} + x y} y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{e^{x y}} e^{x y} = e^{e^{x y} + x y}

= e^{e^{x y} + x y} y

x ∣ x - 2 ∣

x \to - 2 lim (2 ∣ x + 2 ∣)

\frac{\partial}{\partial x} (ln (y + x))

\int_{- 2}^{4} x d x

\int \frac{1}{1 - 3 u} d u

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