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

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

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

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

e^{x + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{x + y} \cdot 1

Simplify

= e^{x + y}

\frac{\partial}{\partial x} (10 x y - 16 x)

\frac{d}{d x} (0.5 x)

x \to - 3 - lim (g (x))

\frac{d}{d x} (\frac{6 x ^{2} + 4 x + 4}{x})

x \to \frac{π}{2} lim (sec (x))

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