How to Find Derivatives Using Limits and Power Rule

TL;DR

To find derivatives using limits, use the limit definition: the derivative of a function f at point x is the limit as h approaches zero of [f(x+h) - f(x)] / h. Additionally, apply the power rule by multiplying the exponent by the coefficient and decreasing the exponent by one. Both methods provide a systematic approach to computing derivatives for various functions.

Transcript

in this video we're going to focus on finding the derivative of a function using the definition of the derivative or the limit process but before we do that let's talk about how to find the derivative the easy way and then we'll do some examples we'll confirm it using limits so let's say if you have x cube what is the derivative of x cubed you can ... Read More

Key Insights

• ✊ The power rule is a method used to find derivatives of functions with exponents.
• ⛔ The limit process involves calculating the difference quotient and taking the limit as the difference approaches zero.
• 0️⃣ Derivatives of constants are always zero.
• ✖️ The derivative of a constant multiplied by a function can be found by differentiating the function and then multiplying it by the constant.
• 👍 The limit process can be used to prove the derivative of a function using the power rule.
• 🫚 The limit process can be used to find the derivative of rational functions and square root functions.

Summary & Key Takeaways

• The video starts by demonstrating how to find derivatives of simple functions using the power rule.

• It then explains how to use the limit process to find the derivative of more complex functions.

• Examples are provided for both methods, showing step-by-step calculations.