What is (\partial)/(\partial x)(e^{x+y+3}) ?

The answer to (\partial)/(\partial x)(e^{x+y+3}) is e^{x+y+3}

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(\partial)/(\partial x)(e^{x+y+3})

\frac{\partial}{\partial x} (e^{x + y + 3})

e^{x + y + 3}

Solution steps

\frac{\partial}{\partial x} (e^{x + y + 3})

Treat

y

as a constant

Apply the chain rule:

e^{x + y + 3} \frac{\partial}{\partial x} (x + y + 3)

= e^{x + y + 3} \frac{\partial}{\partial x} (x + y + 3)

\frac{\partial}{\partial x} (x + y + 3) = 1

= e^{x + y + 3} \cdot 1

Simplify

= e^{x + y + 3}

What is (\partial)/(\partial x)(e^{x+y+3}) ?
The answer to (\partial)/(\partial x)(e^{x+y+3}) is e^{x+y+3}