symmetric derivative

TL;DR

This video explains the concept of symmetric derivatives and how they can be used to find the derivative of functions that are not differentiable at certain points.

Transcript

okay so we all know this right here so you should have finished of the derivative of some function at some point let's say X is equal to a and that's just the critical right here the derivative of some function at a is just the slope of the tangent line at a right and you see we were given this point because you are just talking about the tangent l... Read More

Key Insights

• 😥 The derivative of a function at a point is the slope of the tangent line at that point.
• 🫥 The usual formula for finding the slope of the tangent line requires two points on the function.
• 😥 Symmetric derivatives involve finding the slope of the line between two points on either side of a given point.
• 😥 Symmetric derivatives can be used to find the derivative of functions that are not differentiable at certain points.
• 😥 The symmetric derivative of a function at a point accounts for slopes on both sides of the point.
• ❓ The symmetric derivative of the function |x| at 0 is 0.
• ☺️ The symmetric derivative of the function x + f(x) at 0 is 1.

Questions & Answers

Q: What is the usual formula for finding the slope of the tangent line?

The usual formula is (y2-y1)/(x2-x1), which requires two points on the function.

Q: How does the concept of symmetric derivatives help find the derivative of functions?

Symmetric derivatives involve finding the slope of the line between two points on either side of a given point, allowing for the calculation of the derivative at points where the function is not differentiable.

Q: Can symmetric derivatives be used to find the derivative of functions with corners?

Yes, symmetric derivatives can be used to find the derivative of functions with corners by considering the slopes on both sides of the corner.

Q: What are the symmetric derivatives of the functions |x| and x + f(x) at 0?

The symmetric derivative of |x| at 0 is 0, while the symmetric derivative of x + f(x) at 0 is 1.

Summary & Key Takeaways

• The video discusses the concept of finding the slope of the tangent line using the usual formula of y2-y1 over x2-x1, even when only one point is given.

• The concept of symmetric derivatives is introduced, which involves finding the slope of the line between two points on either side of a given point.

• The video explains how symmetric derivatives can be used to find the derivative of functions that are not differentiable at certain points, such as functions with corners.

• The symmetric derivatives of the functions |x| and x + f(x) at 0 are calculated, resulting in 0 and 1 respectively.