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### Course: AP®︎/College Calculus BC>Unit 3

Lesson 4: Differentiating inverse functions

# Derivatives of inverse functions: from table

Let's delve into the fascinating realm of inverse functions, exploring how to evaluate the derivative of an inverse function, h', at a specific x-value. Using a provided table of values for function g, its inverse h, and its derivative g', we unravel the mystery of h' using the chain rule and the concept of inverse functions.

## Want to join the conversation?

• if f(x) and g(x) are inverse of each other then does it mean that domain of f(x) will be the range of g(x) and range of f(x) will be domain of g(x) and vice versa?
• Simply Yes. That's why they are inverse of each other.
• so h'(x) is undefined when g'(h(x)) is zero ?
• Yes, because g'(h(x))·h'(x)=1. If g'(h(x)) is 0, there is no value of h'(x) that makes the equation true, because it simplifies to 0=1.
• When will I ever be using this after school just wondering?
• Depends on what you do after school. Derivatives are just functions that define the instantaneous rate of change at an input value. This is valuable when dealing with physics in any sense as far as I know, and there are plenty of physics based careers out there.
• What if the value for h(3) was not given and all we had is g'(3) and g(3)? What would we do to solve this then?
• Hi! I was wondering if using Khan Academy for AP exam prep was enough even if you are not taking an actual AP Calc BC course at school. I go to a Canadian high school (so there are no AP classes) and I am taking my exam in May. Are Khan Academy and a prep book enough? Should I take another course?
• You will have to be a very driven and self-motivated student to be successful at this. You certainly can be, but practice regularly and extensively if you want to have a shot. I think having the classroom experience and having a teacher/mentor is definitely an advantage though.
(1 vote)
• are proofs presented in calculus classes?
(1 vote)
• proofs can be presented depending on your teacher but can usually be found in a book
• if h(g(x))=x is the inverse of the function g, does that make g(h(g(x)))=x the inverse of the inverse, and shouldn't the inverse of the inverse just be the original function (g(x))?
(1 vote)
• This isn't really a question about how to do this but I was wondering if derivatives of inverse functions would be still expected on the AP Calculus test (even if there is not a lot). I understand that Sal said that we MIGHT see this in our calculus classes but will it be expected on the AP test? If so, which one? AB or BC or both?
(1 vote)
• As far as I know, the derivatives of inverse functions will be expected on the AP Calculus AB test. You will probably be expected to know the derivatives of inverses on the BC test also since BC is just building off of AP Calculus AB.