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The derivative of the function \( f(x) = \sqrt{7x + 4} \) is:

\[
f'(x) = \frac{7}{2\sqrt{7x + 4}}
\]

Let me know if you have any questions, or if you'd like me to proceed with part (b) of the problem!

Here are some related questions for further exploration:
1. What is the meaning of the derivative in terms of the slope of the tangent line?
2. How do you find the equation of a tangent line at a given point?
3. What happens to the derivative as \( x \) increases?
4. How would you handle finding the derivative of a more complex square root function?
5. Can you interpret the behavior of the graph of \( f(x) \) from the derivative?

**Tip:** Always simplify your derivative as much as possible to make calculations easier!

Find the derivative function f' for the function f. Determine an equation of the line tangent to the graph of f at (a, f(a)) for the given value of a. f(x) = √(7x + 4), a = 3

Learn how to find the derivative function of f(x) = √(7x + 4) and determine the equation of the tangent line at a given point. This problem covers key calculus concepts, including the derivative of square root functions and the equation of tangent lines, suitable for Grades 11-12.

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