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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

\int (1 - y^{2}) d y

y^{^{''}} + 7 y^{^{'}} + 10 y = - 18 t e^{2 t}

x \to 0 lim (\frac{0}{x ^{2}})

\frac{0.9 e ^{x}}{tan ( x )}

\int_{6}^{8} \frac{6}{( x - 6 ) ^{3}} d x

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