Question

f(x)=e^x+x and its inverse is g(x). Calculate g'(1)

Answer 1

have you found the inverse?

Answer 2

I know d/dx e^x is e^x.

Answer 3

the inverse is just 1/(e^x+x) i beleive

Answer 4

\[f(x)=e^{x}+x\] is your equation right?

Answer 5

yeah

Answer 6

the inverse of differentiation is integration, or finding the antiderivative

anti derivative of x is x^2/2, so that when you differentiate it you get x back

Answer 7

problem is because we have not covered that part in class yet we cant use in in our solution.

Answer 8

that and I have no idea what you mean by the antiderivative

Answer 9

so in fact you dont need to do any integration here, pay close attetion to the question g'(x) = f(x)

so all you need to do is eval f(1) to get g'(1)

Answer 10

hmm then just throw it over 1, but in this case it will still be 1

Answer 11

g'(1)=f(1)=e+1

Answer 12

well here let me scan the question as thats what I did but apparently its wrong

Answer 13

@k1dj03y it states that g(x) is the inverse not the derivative

Answer 14

f(x)=e^x+x and its inverse g(x). Calculate g'(1)

Answer 15

oops i added the word is to that question.

Answer 16

it's still the same thing, the question tells you that the inverse of f(x) is g(x)

Answer 17

so if you differentiate the inverse function you will get the original function back, which is f(x)

Answer 18

hmm thats just it then as when it was graded i only received 3/10 possible for the solution.

Answer 19

@arjont you are thinking of intergration that is not what the relationship between f(x) and g(x) is

Answer 20

http://www.wolframalpha.com/input/?i=inverse+function

Answer 21

Im attaching the question and what I received back as feedback to see if it helps things

Answer 22

The graph may make things look better as he gives us g(x) in the form of a graph. Which also happens to be the inverse of (f(x)) if I am understanding things right

Answer 23

I could just look at the graph and be like there it is, but, it asks for it to be calculated. . .

Answer 24

I think this is the formula your teacher wanted you to use \[[f ^{-1}]\prime(a)=\frac{ 1 }{ f \prime(f ^{-1}(x)) }\] look familiar?

Answer 25

somewhat yeah

Answer 26

well you can solve for g(1) without finding the inverse function. You can also calculate the derivative of f(x) plug them into that equation and you should get you answer

Answer 27

@k1dj03y I made a mistake typing my question that x variable should be a, sorry about that

Answer 28

yeah we have been using u but its the same idea so i understood where it was going at least

Answer 29

do you need more help are do you think you are good with this question now?

Answer 30

naw I think I can take it from there thx bunches

Answer 31

Okay don't forget to close the question.

Answer 32

haha yeah I was going to. Just hate cutting people off mid typing

Answer 33

@arjont do you want/need further explanation?

Answer 34

no, i didnt know what he meant by g' i thought it was the derivative

Answer 35

they do want you to find the value of the derivative of the inverse at one. Its just an error in reading the question then.