The given function is $f(x) = 5x + 1$. To find $f'(a)$, where $a = 3$, we need to first compute the derivative of $f(x)$, then substitute $a = 3$.

Step 1: Compute the derivative $f'(x)$

Since $f(x) = 5x + 1$, the derivative is: $f'(x) = 5$ This is because the derivative of $5x$ is 5, and the derivative of a constant (1) is 0.

Step 2: Evaluate the derivative at $a = 3$

Since $f'(x) = 5$, the derivative does not depend on $x$, so: $f'(3) = 5$

Thus, $f'(3) = 5$.

Would you like further details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the derivative of a linear function in general?
2. How does the value of $f'(x)$ change for functions like $f(x) = ax + b$?
3. How would you interpret $f'(a)$ geometrically?
4. How do you find the derivative of a more complex polynomial function?
5. What happens to the derivative if the function contains higher powers of $x$?

Tip: The derivative of any constant term in a function is always zero, as constants do not change with $x$.