03. Derivative using definition as limit

Takeaways

• 😀 The video explains how to calculate the derivative of the function f(x) = 5x using the definition of a derivative.
• 😀 The definition of a derivative is based on the limit formula, which is outlined at the beginning of the video.
• 😀 The process involves substituting x + h into the original function and simplifying the result step by step.
• 😀 After substitution, the next step is to calculate the difference and simplify the fraction as much as possible.
• 😀 The key simplification involves canceling out terms like 5x - 5x, which results in the fraction 5h/h.
• 😀 Dividing h by h simplifies to 1, leaving a result of 5 as the derivative of the function f(x) = 5x.
• 😀 Once simplified, there is no h left in the expression, so the limit simply evaluates to 5.
• 😀 The result of the derivative calculation is that the derivative of the function f(x) = 5x is 5.
• 😀 The video encourages viewers to practice calculating the derivative of similar functions, such as f(x) = 2x, 8x, or 20x.
• 😀 Viewers are invited to verify their results by watching the next video, which will cover the procedure for calculating derivatives in more detail.
• 😀 The video concludes with a call to action, encouraging viewers to like, subscribe, and share the content while leaving questions or suggestions in the comments.