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

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

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

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

e^{y}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= e^{y} + 0

Simplify

= e^{y}

f (x) = \frac{5}{x}

x \to 0 lim (e^{3} - e^{x + 3})

\int_{1}^{7} \frac{6}{x ^{2}} d x

t^{2} y^{^{''}} - 2 y = 6 t^{2} - 1

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

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