Question

prove d/dx(arccosh x) = 1/sqrt(x^2-1) implicitly

thanks (:

Answer 1

Hoot! You just asked your first question! Hang tight while I find people to answer it for you. You can thank people who give you good answers by clicking the 'Good Answer' button on the right!

Answer 2

\[y=\cos^{-1} x\]??

Answer 3

hyperbolic eh...shudder

Answer 4

Let arcosh(x) = y
cosh(y) = x
(d/dx)(cosh(y)) = (d/dx)(x)
sinh(y) * (dy/dx) = 1
(dy/dx) = 1/sinh(y)

;;; cosh²(y) - sinh²(y) = 1,

;;; sinh(y) = sqrt(cosh²(y) - 1) = sqrt(x² - 1)

Hence, if y = arcosh(x),
(d/dx)(arcosh(x)) = dy/dx = 1/sqrt(x² - 1)

Answer 5

thanks!