# Derivative using the Limit Definition (Quadratic Example) | Summary and Q&A

564 views
β’
August 19, 2020
by
The Math Sorcerer
Derivative using the Limit Definition (Quadratic Example)

## TL;DR

This video explains how to find the derivative of a function using the limit process.

## Key Insights

• π The derivative of a function can be calculated using the limit process and the formula f'(x) = (f(x + h) - f(x)) / h.
• βΊοΈ Memorizing the formula for expanding (x + h)^2 can simplify calculations.
• π Canceling out terms with opposite signs is crucial in simplifying the expression.
• π» Factoring out h from the numerator allows for the substitution of h with zero to find the derivative.

## Transcript

hi everyone in this problem we're going to find the derivative of this function using the limit process so the formula for the derivative is the following so f prime of x is equal to the limit as h approaches 0 of f of x plus h minus f of x all divided by h so all we have to do in this problem is work this out and we should be good to go so this is... Read More

### Q: What is the formula for finding the derivative using the limit process?

The formula is f'(x) = (f(x + h) - f(x)) / h, where f'(x) is the derivative of f(x).

### Q: How do you replace x with x + h in the given function?

To replace x with x + h, you substitute x in the function with x + h. For example, x^2 becomes (x + h)^2.

### Q: Why do some terms cancel out during the simplification process?

Terms cancel out because they have the same value but opposite signs, such as -x^2 canceling out x^2.

### Q: How do you find the derivative after simplification?

After simplifying and canceling out terms, you factor out h from the numerator and then replace h with zero to find the final derivative, which is 2x + 1.

## Summary & Key Takeaways

• The video explains the formula for finding the derivative using the limit process.

• It uses a specific function, f(x) = x^2 + x - 5, as an example.

• The process involves replacing x with x + h, simplifying the expression, canceling out terms, and factoring out h to find the derivative.