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

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

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

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

e^{y}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + e^{y}

Simplify

= e^{y}

y^{^{''}} - 2 y^{^{'}} - y = 0, y (0) = 0, y^{^{'}} (0) = 22

1

y = e^{4 x}, at x = \frac{1}{4} ln (5)

\frac{d}{d x} ((4 + 8 x) cosh (2 x))

5 \cdot sin (2 \cdot t)

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