Question

How do you differentiate `y = cos^-1 (e^-t)`?

Answer 1

Differentiate implicitly.

Explanation:

`y=cos^-1 (e^(–t))`
`cos y = e^(–t)`

Differentiating wrt `t`:
`–sin y dy/dt = –e^(–t)`
`–sqrt(1-cos^2 y) dy/dt = –e^(–t)`
`–sqrt(1-e^(–2t)) dy/dt = –e^(–t)`
`dy/dt = e^(–t) / sqrt(1-e^(–2t))`