How to take the derivative of the inverse of a function

The video tutorial covers the concept of inverse functions and their derivatives. It begins with an introduction to the problem, explaining the relationship between a function and its inverse. The tutorial then delves into calculating the derivative of an inverse function, using specific examples and the power rule. Throughout the video, the instructor provides clarifications and corrections to ensure understanding. The lesson concludes with a summary of the key points discussed.

What is the relationship between f(0) = 2 and its inverse function?

• f inverse of 2 equals 1

• f inverse of 1 equals 0

• f inverse of 0 equals 2

• f inverse of 2 equals 0

How do you find the derivative of the inverse function at a point?

• By adding 1 to the derivative of the original function

• By multiplying the derivative of the original function by 2

• By subtracting 1 from the derivative of the original function

• By taking the reciprocal of the derivative of the original function at the corresponding point

What mistake was corrected regarding the derivative calculation?

• The power rule was applied incorrectly

• The inverse function was not considered

• The derivative was calculated at the wrong point

• The variables were swapped incorrectly

What is the result of applying the power rule to the function 2x^4 + x^2 + 3?

• 4x^3 + 2x

• 8x^3 + 2x

• 8x^3 + x

• 4x^3 + x

What is the value of f prime of 0 for the function 2x^4 + x^2 + 3?

• 1

• 3

• 2

• 0