The function given is:

\[
f(x) = e^x - e^{-x}
\]

To find the derivative, we will differentiate each term separately using the basic rules of differentiation:

1. The derivative of \( e^x \) with respect to \( x \) is \( e^x \).
2. The derivative of \( e^{-x} \) with respect to \( x \) is \( -e^{-x} \) (using the chain rule).

Thus, the derivative \( f'(x) \) is:

\[
f'(x) = \frac{d}{dx} \left( e^x - e^{-x} \right) = e^x + e^{-x}
\]

So, the derivative of \( f(x) = e^x - e^{-x} \) is:

\[
f'(x) = e^x + e^{-x}
\]

Would you like more details on any specific step or further explanation?

Here are 5 related questions to expand on this:

1. What is the second derivative of \( e^x - e^{-x} \)?
2. How would you find the derivative of \( e^{2x} \)?
3. How does the chain rule apply when differentiating functions like \( e^{-x} \)?
4. What is the derivative of \( e^x \sin(x) \)?
5. How would you compute the derivative of \( e^x \) multiplied by a polynomial?

**Tip:** The exponential function \( e^x \) has the unique property of being its own derivative!

Discover how to find the derivative of e^x - e^-x in this detailed solution. This problem covers key calculus concepts such as differentiation, exponential functions, and the chain rule. Suitable for students in Grades 11-12 or introductory college calculus.

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