Question

How do you find the derivative of `y = arccos(e^(5x))`?

Answer 1

`(-5e^(5x))/sqrt(1-e^10x), x<=0`.

Explanation:

`cos y=e^(5x)`.
`(-sin y) y'=5e^(5x)`.
`y'=-(5e^(5x))/(1-cos^2y`
`=.-(5e^(5x))/(1-e^(10x)`
Note that if x>0, `e^(5x)>1`, cos y > 1 and y becomes unreal.