dy/dx, d/dx, and dy/dt - Derivative Notations in Calculus

TL;DR

The video explains the difference between dy/dx and d/dx in terms of what they mean and how to use them in differentiation problems.

Transcript

in this video i kind of want to discuss the difference between dydx and also d over dx because when dealing with derivatives typically you'll see these two things and you might be wondering what to do when you see them well let's say that y is equal to x cubed plus 4x what does it mean when you see dydx in a problem like this and sometimes you'll s... Read More

Key Insights

• 🐞 dy/dx represents the derivative of a function y with respect to x, while d/dx is a command to differentiate a function with respect to x.
• ✊ Both dy/dx and d/dx can be used to find derivatives using the power rule.
• 🐞 In implicit differentiation, when differentiating a function with variables that don't match, dy/dx needs to be included in the solution.

Questions & Answers

Q: What is the difference between dy/dx and d/dx?

The difference lies in their meaning and usage. dy/dx represents the derivative of a function y with respect to x, while d/dx is a command to differentiate a function with respect to x.

Q: How do you use dy/dx and d/dx in differentiation problems?

dy/dx is used to directly find the derivative of a function y with respect to x, while d/dx is used to differentiate a function inside the brackets with respect to x.

Q: Can dy/dx and d/dx be used with different variables?

Yes, in related rates problems, they can be differentiated with respect to different variables, such as t or s.

Q: What is implicit differentiation?

Implicit differentiation is used when differentiating functions that have variables that do not match. It involves using the power rule and including dy/dx in the solution.

Summary & Key Takeaways

• The video discusses the difference between dy/dx and d/dx in terms of their meanings and usage in differentiation problems.

• dy/dx represents the derivative of a function y with respect to x, while d/dx is a command to differentiate a function with respect to x.

• Both dy/dx and d/dx can be used to find derivatives using the power rule, and in related rates problems, they can be differentiated with respect to different variables, such as t or s.