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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Apply exponent rule:

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

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

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

f^{^{'}} (x) = 7 e^{- e} - 5 e^{- 7 x}

x \to 0 + lim (\frac{3}{1 + e ^{\frac{1}{x}}})

\int \frac{4}{1 + 9 x ^{2}} d x

\int - x^{5} d x

\int \frac{2 u}{4 u ^{2} + 3} d u

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