derivative of x^-2 with the definition of derivative

TL;DR

The video demonstrates how to find the derivative of 1/x^2 using the definition of derivative.

Transcript

we will find the derivative of 1/x^2 by using the definition of derivative prime of a by using the definition of derivative  i will use the second derivation of derivative   in other words we have to find the limit as h  goes to zero f of a plus h minus f of a or over h   so we have to figure out what the f of a plus  h is first so let's do the out... Read More

Key Insights

• 🎮 The video demonstrates how to find the derivative of 1/x^2 using the definition of derivative.
• 😑 The process involves expanding the expression and canceling out terms to simplify the final result.
• 😥 Taking the limit as h approaches zero helps find the instantaneous rate of change at a specific point.

Questions & Answers

Q: How do you find the derivative of 1/x^2?

The derivative of 1/x^2 can be found using the definition of derivative. By taking the limit as h approaches zero, the expression is expanded and simplified to find the derivative. The final answer is -2/a^3.

Q: What is the purpose of using the definition of derivative in this problem?

Using the definition of derivative allows us to find the derivative of any function. In this problem, it helps us find the derivative of 1/x^2 by breaking it down into smaller steps and simplifying the expression.

Q: How does the process of canceling out terms work?

When multiplying out the expression, certain terms cancel each other out. For example, -a^2 + a^2 equals zero, so those terms disappear. By canceling out terms, the expression is simplified and the final answer is obtained.

Q: What is the significance of taking the limit as h approaches zero?

The limit as h approaches zero allows us to find the instantaneous rate of change at a specific point. In this problem, it helps us find the derivative of 1/x^2 at the point where x = a.

Summary & Key Takeaways

• The video explains how to find the derivative of 1/x^2 using the definition of derivative.

• By using the limit as h approaches zero, it breaks down the equation step-by-step.

• The process involves expanding the expression and canceling out terms to simplify the final result.