What is (\partial)/(\partial x)(e^x*e^y) ?

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

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(\partial)/(\partial x)(e^x*e^y)

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

e^{x + y}

Solution steps

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

Simplify

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

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x + y} \cdot 1

Simplify

= e^{x + y}

\frac{d}{d x} (\frac{( x + 1 ) ^{2}}{3 x - 4})

\int \frac{4}{x - 6} d x

3 x y^{^{'}} - 3 y = x^{- 7}

\frac{d}{d x} (x^{3} - 5 a x^{2} + 3 a^{2} x + b)

\int \frac{1}{u ^{2} - 1} d u

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