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Let's solve the given problem step by step.

The function is 
\[
f(x) = 20e^x - e^x.
\]

### Step 1: Find the derivative \(f'(x)\).

First, let's rewrite the function:
\[
f(x) = (20 - 1)e^x = 19e^x.
\]

Taking the derivative with respect to \(x\), we have:
\[
f'(x) = 19e^x.
\]

### Step 2: Evaluate \(f'(3)\).

Substituting \(x = 3\):
\[
f'(3) = 19e^3.
\]

Hence, the answer is:
\[
f'(3) = 19e^3.
\]

Would you like further details or explanations on this solution?

### Here are 5 related questions to expand your understanding:
1. What is the derivative of \( f(x) = ae^x \), where \(a\) is any constant?
2. How would you find \( f'(x) \) if the original function had multiple terms, like \( f(x) = e^x + 5e^{2x} \)?
3. What is the significance of the natural exponential function \(e^x\) in calculus?
4. Can you apply the product rule to functions like \( f(x) = x^2e^x \)?
5. What would happen if the original function was \( f(x) = 20e^{2x} - e^x \)?

**Tip:** When differentiating exponential functions, always remember that the derivative of \(e^x\) with respect to \(x\) is simply \(e^x\).

Suppose that f(x) = 20e^x - e^x. Find f'(3).

Learn how to find the derivative of f(x) = 20e^x - e^x and calculate f'(3). This problem involves key calculus concepts such as derivatives of exponential functions, providing a step-by-step solution suitable for Grades 10-12.

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