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

The answer to (\partial)/(\partial x)(e^{e^yx+y}) is e^{e^yx+2y}

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

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

e^{e^{y} x + 2 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

e^{e^{y} x + y} e^{y} : e^{e^{y} x + 2 y}

= e^{e^{y} x + 2 y}

f (x) = 4 x^{2} + 6 x + 3

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What is (\partial)/(\partial x)(e^{e^yx+y}) ?
The answer to (\partial)/(\partial x)(e^{e^yx+y}) is e^{e^yx+2y}