derive the formula d(sinh^-1 z)/dz=1/(1+z^2)^1/2 also i know there needs to be certain conditions that make this possible

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- Mar 9th 2009, 04:25 PMHongoshderiving the formula
derive the formula d(sinh^-1 z)/dz=1/(1+z^2)^1/2 also i know there needs to be certain conditions that make this possible

- Mar 9th 2009, 06:59 PMmanyarrows
I was just doing these for class last unit. You have to use the formula for deriving Inverse functions 1/f ' (g(x)) where f(x) is the inverse of g(x). In this case f (x)=sinch x and g(x)=arcsinch x (I don't know if it is legal to call it arcsinch, but I don't know how to write the math formulas on the computer) Anyway after this use the identity

cosh x= (1-(sinch x)^2)^1/2). try it from there and keep in mind it is similar to deriving inverse trig functions. - Mar 9th 2009, 09:24 PMmr fantastic
- Mar 10th 2009, 06:56 AMSoroban
Hello, Hongosh!

A variation of Mr. F's solution . . .

Quote:

Derive the formula: .

We have: . .[1]

Differentiate implicitly: . .[2]

Substitute [1]: .

Substitute into [2]: .