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

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

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

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

e^{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (e^{y}) = 0

= e^{x} + 0

Simplify

= e^{x}

\int (\frac{3}{x ^{4}}) d x

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

\frac{\partial}{\partial x} (4 x + 9 y - 360)

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

f (x) = x^{3} + 9 x^{2} + x + 9

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