Differentiate the function $$ g\left(x\right)+=e^{x+2} $$$$ +2. $$

It seems like there might be a small error in your function notation. Based on what you've provided, I assume you're asking to differentiate the function:

\[
g(x) = e^{x+2} + 2
\]

Let's differentiate this with respect to $x$.

### Steps:
1. The derivative of $e^{x+2}$ with respect to $x$ is simply $e^{x+2}$, because the exponential function's derivative is the same as the function itself.
2. The derivative of the constant $2$ is $0$, as constants have a zero derivative.

### Solution:
\[
g'(x) = \frac{d}{dx}\left(e^{x+2} + 2\right) = e^{x+2} + 0 = e^{x+2}
\]

Thus, the derivative is:

\[
g'(x) = e^{x+2}
\]

Would you like any further details or have any questions?

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Here are 5 related questions for you to explore:
1. How do you differentiate a function with multiple terms, like polynomials?
2. What is the derivative of a function involving $ \ln(x) $?
3. How does the chain rule apply to more complex exponentials, such as $ e^{f(x)} $?
4. How would you find the second derivative of $ g(x) $?
5. What happens if you differentiate a product of functions?

**Tip:** When differentiating exponentials, always watch out for whether a chain rule is necessary if the exponent is more complex than a linear function of $x$.

Learn how to differentiate the function g(x) = e^(x+2) + 2 step-by-step. This problem covers differentiation of exponential functions and constants. Suitable for advanced high school students and anyone studying calculus.

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