Question

How do I find the derivative of an inverse of a function?

I don't know how and what to plug into the formula.

Answer 1

http://tutorial.math.lamar.edu/Classes/CalcI/DiffInvTrigFcns.aspx

Answer 2

I'd answer your question exactly, but I'm going to need an example problem to work with :)

Answer 3

Thank you so much!!!! :)))) I've looked and looked on Google and the only one I had done got the same wrong answer as me lol. Unless my book is wrong but I doubt it :s



the problem is f(x) = 2x^3 + 3x^2 +7x + 4 a=4

Answer 4

x=a=4?

Answer 5

yes :)

Answer 6

I don't know why they couldnt keep the same variables. My books uses "a" in the formula so they just kept it that way for everything

Answer 7

so f(a)=208

You seek to find d/dx (f^-1(x)) right?
or just the value for a?

Answer 8

Right. I need to find the derivative of the inverse :)

Answer 9

is f(c)=a, or is x=a?

Answer 10

x=a :)

Answer 11

ahh, been way too long since I've done this, @ranga , if you got it, you'll probably come up with it faster than I will...

Answer 12

Are you sure the question is not find the derivative of the inverse of f(x) at x = a given that
\[\Large f ^{-1}(a) = 4\]?

Answer 13

"Find (f^-1)' (a)

Answer 14

Yes. That agrees with the first part: find the derivative of the inverse of f(x) at x = a but what about the inverse of f at x = a is 4?

Answer 15

It does not give any value amount besides that a=4. I'm supposed to find everything based on the given 4.

Answer 16

This is the standard formula for evaluating the derivative of an inverse at x = a given the value of the inverse function at x = a:
\[\Large [f ^{-1}]'(a) = \frac{ 1 }{ f'(f ^{-1}(a))}\]

Answer 17

Right :) I'm just not sure what goes where. When I solved it the way I *thought* I got 1/127. The book says the answer is 1/7.

I swapped the x and y values and solved the equation for x.
I then took the derivative of that so dx/dy.

But I needed it in terms of y so I swapped the derivative to dy/dx which made the other side of the equation flip. So my 6y^2 +6y + 7 became 1/6y^2 +6y + 7 But thats wrong and I dont know why.

Answer 18

And you have copied the problem here exactly the way it appears in the book? You may want to double check.

Answer 19

I have :) There are no directions besides the Find (f^-1)' (a) and the problem.

Answer 20

Try this. Find f inverse and evaluate it at x = a = 4. Then take that value and plug it into the formula I gave above.

Answer 21

Thank you so so much for your help!! :) I GREATLY appreciate it!!

Answer 22

Did you get 1/7? Because this is a cubic equation and finding the inverse is not easy.

Answer 23

I honestly haven't gotten past that part, but I see what you're saying once I do get that answer :)

Answer 24

Normally we are given the x value and we are asked to find the y value.

In inverse function, we are given the y value and asked what x would gives us that y value.

f(x) = 2x^3 + 3x^2 +7x + 4

We need to find f(^-1)(4). It means what value of x will make f(x) = 4

4 = 2x^3 + 3x^2 +7x + 4
2x^3 + 3x^2 +7x = 0
x(2x^2 + 3x + 7) = 0.
So x = 0 will make f(x) 4
So f^-1(4) = 0

Put x = 0 in the derivative of the inverse: 1 / (6x^2 +6x + 7) and you get 1/7

Answer 25

You have no idea how thankful I am for this answer!! Thank you so much! :) I have a test Monday and I'm so confused with this stuff.

I got to the factor out part like you did and ended up getting -3 (+/-) sqrt -47 etc.
I couldn't figure out how I would have an imaginary number in my answer...
thank you so much for your time and help!!! this helps me so much!! :)

Answer 26

It is a cubic equation and it has three roots. Only one is real at x = 0 and the other two are imaginary which you can discard.

Glad to be able to help. Good luck in the test.

Answer 27

Thank you so much! :)))) I greatly appreciate it! :))

Answer 28

You are welcome.