Question

How do you differentiate `y=csc^-1(e^x)`?

Answer 1

`dy/dx = - tan (csc^-1 (e^x))`

Explanation:

`csc y = e^x => ln (1/sin y) = x`

`dx/dy = sin y * (-1/sin^2 y) * cos y`

`dy/dx = (dx/dy)^-1 = -sin y / cos y = - tan (csc^-1 (e^x))`