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

The answer to (\partial)/(\partial x)(e^y+x) is 1

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

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

1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 0 + 1

Simplify

= 1

\frac{d}{d x} ((6^{\frac{2}{3}} - x^{\frac{2}{3}})^{\frac{3}{2}})

\int \frac{1}{x ^{2} + x + 5} d x

\int e^{3 x - 2} d x

\frac{d y}{d x} - 9 y^{2} e^{- 1 x} = 0, y (0) = 5

y = x^{4}, at x = 0

What is (\partial)/(\partial x)(e^y+x) ?
The answer to (\partial)/(\partial x)(e^y+x) is 1