Derivative of Inverse Trig & Hyp

[Guest]

I'm looking for the method of finding the derivative of arcsinx and arccoshx, can anyone help? I know that coshx can be derived using its exponenial form, but I don't have a clue for arccoshx, as for sinx, thats easy to derive but arcsinx just stumps me! I just want the method not a solution because its homework :lol: Help would be greatly appreciated.
Cheers
Josh

 

[Guest]

I THINK, I have it, do you take the arcsin (or arccosh) over the other side and differentiate implicitly with respect to x, then fiddle around with it to get dy/dx by itself, and finally sub y=arcsinx back into anywhere where y is in the equation?

 

[Unco]

You should know that (d/dx)cosh(x) = sinh(x).

To find (d/dy)arccosh(y), use the fact that
(d/dx) cosh(x) * (d/dy) arccosh(y) = 1.

See if you can put it back in terms of a hyperbolic function of y (hint: use the hyperbolic analogue of the trig identity cos^2(x)+sin^2(x)=1 )

 

[Unco]

I THINK, I have it, do you take the arcsin (or arccosh) over the other side and differentiate implicitly with respect to x, then fiddle around with it to get dy/dx by itself, and finally sub y=arcsinx back into anywhere where y is in the equation?

Good work. The last bit of my post may be of help to you for the last job.