Understanding Derivatives of Inverse Functions

This video tutorial explains how to find the derivative of an inverse function. It begins with an introduction to the concept and the formula used for calculation. The video then delves into understanding inverse relations and how coordinates are switched. It provides a detailed walkthrough of calculating derivatives using both a formula and implicit differentiation. Finally, an example problem is solved to reinforce the concepts learned.

What is the formula for the derivative of an inverse function?

• 1 over the derivative of the original function

• The derivative of the original function

• The square of the original function

• The inverse of the original function

In inverse relations, if the original point is (3, 7), what is the inverse point?

• (3, 7)

• (7, 7)

• (3, 3)

• (7, 3)

If x2 is 11, what is the corresponding y1 in the inverse relation?

• 11

• 2

• 7

• 3

What is the derivative of the function f(x) = x^3 + 3 at x = 2?

• 10

• 8

• 6

• 12

Using implicit differentiation, what is the derivative of the inverse function when y2 is 2?

• 1/6

• 1/12

• 1/10

• 1/8

What is the first step in verifying the derivative using implicit differentiation?

• Solve for dy/dx

• Factor out dy/dx

• Switch x and y

• Differentiate both sides

In the new example, what is the value of x1 when y1 is 3?

• 1

• 2

• 3

• 4

What is the derivative of the function f(x) = x^3 + 4x - 2 at x = 1?

• 7

• 5

• 9

• 11

What is the final answer for the derivative of the inverse function in the new example?

• 1/11

• 1/9

• 1/5

• 1/7

What method can be used to confirm the derivative of an inverse function?

• Explicit differentiation

• Graphical differentiation

• Numerical differentiation

• Implicit differentiation