What is (\partial)/(\partial x)(e^ye^x) ?

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

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(\partial)/(\partial x)(e^ye^x)

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

e^{y + x}

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (y + x) = 1

= e^{y + x} \cdot 1

Simplify

= e^{y + x}

\frac{\partial}{\partial x} (y e^{- 2 x})

- 2 t

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

\int_{0}^{1} v^{2} cos (v^{3}) d v

\frac{d}{d x} ((\frac{d}{d x} (x^{3}))^{2})

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