Question

derivative of e^(cos^-1(x))

Answer 1

d/dx(e^(cos^(-1)(x))) = -e^(cos^(-1)(x))/sqrt(1-x^2)

Answer 2

http://www.wolframalpha.com/input/?i=derivative+e%5E%28cos%5E-1%28x%29%29

Answer 3

y=e^(arccos(x))
take antilog on both side
lny=arccos(x)
1/y y'=1/sqrt(1-x^2)
so y'=e^(arccos(x)) /sqrt(1-x^2)