(Q23.) So, you think you can take the derivative?

TL;DR

This video explains how to find the derivative of tangent of e to the x over x plus 1 using the quotient rule.

Transcript

all right 23 we are going to take the derivative of tangent of e to the x over x plus 1. and here is the key you need to know what's the derivative of tangent so we have to remember the table the derivative of the tangent is secant squared so we are going to begin by writing this down as secant squared of the inside stays the same of the inside whi... Read More

Key Insights

• ❎ The derivative of tangent is secant squared.
• ☺️ The derivative of e to the x is e to the x.
• ☺️ The product rule and quotient rule are used to find the derivative of tangent of e to the x over x plus 1.
• 😑 Simplifying the expression step by step helps in finding the derivative efficiently.

Questions & Answers

Q: What is the derivative of tangent?

The derivative of tangent is secant squared.

Q: How can we find the derivative of tangent of e to the x over x plus 1?

We can find the derivative by first applying the product rule and then simplifying the expression step by step.

Q: What is the derivative of e to the x?

The derivative of e to the x is just e to the x.

Q: How do we apply the quotient rule in finding the derivative of tangent of e to the x over x plus 1?

To apply the quotient rule, we square the denominator, multiply it with the derivative of the numerator, and subtract the numerator multiplied by the derivative of the denominator.

Summary & Key Takeaways

• The video teaches how to find the derivative of tangent of e to the x over x plus 1 using the quotient rule.

• The derivative of tangent is secant squared.

• The derivative of e to the x is just e to the x, and the derivative of x is 1.