y=sinx+cosx is a function defined in the interval [0,pi/6], find derivative of f^-1(x)?
[QUOTE=hollywood;787266]You have so should be . I don't see how you get . Are you sure the problem and answer are both copied correctly?
I follow you on the second line of your post. On the third line you should have instead of giving .
y^2=1+sin2x, f^-1(x)=1/2.arcsin(x^2-1),x/(2x^2-x^4)
Oh, sure enough. It should be , and then you can cancel x giving .
In my solution I forgot to swap y and x, so I should have had , which gives the same thing if you substitute (after a lot of algebra). Your solution is more direct. Well done.
- Hollywood