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The given function is \( f : x \mapsto e^{2x - 7} \), and we are asked to find its derivative.

To differentiate this function, we apply the chain rule, which states that the derivative of \( e^{g(x)} \) is \( e^{g(x)} \cdot g'(x) \), where \( g(x) \) is the inner function.

In our case, \( g(x) = 2x - 7 \), so let's compute the derivative:

1. The derivative of \( g(x) = 2x - 7 \) is \( g'(x) = 2 \).

Now, applying the chain rule:
\[
f'(x) = e^{2x - 7} \cdot 2 = 2e^{2x - 7}.
\]

Thus, the derivative of the function is:
\[
f'(x) = 2e^{2x - 7}.
\]

Would you like a more detailed explanation or have any further questions?

Here are 5 related questions you might find helpful:
1. How do you apply the chain rule to more complex functions?
2. What is the derivative of other exponential functions like \( e^{x^2} \)?
3. How can the chain rule be used in multivariable calculus?
4. What is the geometric interpretation of the derivative of an exponential function?
5. How does the constant \( e \) influence the behavior of the function and its derivative?

**Tip:** Always remember to first identify the inner function when applying the chain rule.

Soit la fonction f définie ci-dessous : f : x -> e^(2x - 7). Déterminer la dérivée de f. On admettra qu'elle est dérivable sur R.

Learn how to differentiate the exponential function f(x) = e^(2x - 7) using the chain rule. This detailed step-by-step solution explains the chain rule and applies it to find the derivative. Suitable for high school students in Grades 10-12.

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