Question

How do you find the derivative of the function: `y = arccos[e^(2x)]`?

Answer 1

`y'=-(2e^(2x))/sqrt(1-e^(4x))`

Explanation:

Using the arccosine formula in conjunction with the chain rule:

`d/dx[arccos(u)]=-(u')/sqrt(1-u^2)`

Thus,

`y'=-(d/dx[e^(2x)])/sqrt(1-(e^(2x))^2)=-(2e^(2x))/sqrt(1-e^(4x))`