y=sinx+cosx is a function defined in the interval [0,pi/6], find derivative of f^-1(x)?

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- May 15th 2013, 06:58 AMkastamonudifferential
y=sinx+cosx is a function defined in the interval [0,pi/6], find derivative of f^-1(x)?

- May 15th 2013, 08:08 AMhollywoodRe: differential
The derivative of is .

- Hollywood - May 15th 2013, 11:01 PMkastamonuRe: differential
Yes it is but I couldn't find the answer given by this method.

- May 15th 2013, 11:12 PMkastamonuRe: differential
I couldn't find the answer. Answer is 1/sqrt(2-x^2)

y^2=1+sin2x y=sqrt(1+sin2x) and if we differentiate y, and write it

1/dy/dx, we find 1/cosx/sqrt(1+sin2x). - May 16th 2013, 07:52 AMhollywoodRe: differential
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 .

- Hollywood - May 16th 2013, 08:34 AMkastamonuRe: differential
[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) - May 16th 2013, 09:17 AMhollywoodRe: differential
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