Derivative of f(t) = cos(t)/t using the Quotient Rule

TL;DR

This video explains how to find the derivative of a function using the quotient rule.

Transcript

in this problem we're going to use something called the quotient rule to find the derivative so the formula for the quotient rule is the following so if you have a function which i'll call f and you divide it by g and you take the derivative it's the derivative of the top function which is f times the bottom function minus the top function times th... Read More

Key Insights

• 🗂️ The quotient rule is a useful tool for finding the derivative of a function divided by another function.
• ✖️ When applying the quotient rule, it is important to differentiate the top function, multiply it by the bottom function, subtract the top function multiplied by the derivative of the bottom function, and divide it by the bottom function squared.
• 🍉 Factoring out common terms in the numerator can help simplify the expression and cancel out terms for a cleaner derivative.

Questions & Answers

Q: What is the quotient rule?

The quotient rule is a formula used to find the derivative of a function that is divided by another function. It states that the derivative is the derivative of the top function times the bottom function minus the top function times the derivative of the bottom, all divided by the bottom function squared.

Q: How do you find the derivative of cosine t using the quotient rule?

To find the derivative of cosine t using the quotient rule, we differentiate the top function, which is cosine t (resulting in negative sine t), multiply it by the bottom function, t^7, subtract the top function cosine t multiplied by the derivative of the bottom function (7t^6), and divide it by the bottom function squared (t^14).

Q: Why do we factor out t^6 in the numerator?

We factor out t^6 in the numerator to simplify the expression. By doing so, we can cancel out t^6 terms in the numerator and denominator, resulting in a simpler form of the derivative.

Q: What is the final expression for the derivative of the function?

The final expression for the derivative of the function is -tsin(t) - 7cos(t) divided by t^8.

Summary & Key Takeaways

• The video introduces the quotient rule for finding the derivative of a function.

• It demonstrates applying the quotient rule to a specific function.

• The final step involves simplifying the expression by factoring out common terms and canceling out.