What is (\partial)/(\partial x)(e^{x+y}-1) ?

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

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(\partial)/(\partial x)(e^{x+y}-1)

\frac{\partial}{\partial x} (e^{x + y} - 1)

e^{x + y}

Solution steps

\frac{\partial}{\partial x} (e^{x + y} - 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (1) = 0

= e^{x + y} - 0

Simplify

= e^{x + y}

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

\frac{d}{d x} (4 x^{\frac{5}{2}})

x \to - 2 lim (\frac{2 + ∣ x ∣}{2 + x})

\frac{d}{d x} (\frac{arcsin ( x )}{sin ( x )})

x \to 0 lim (\frac{x ^{4}}{x})

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