Question

How do you find the derivative of the function `y = arccos(e^(3x))`?

Answer 1

`y'=(3e^(3x))/(sqrt(1-e^(6x))`
Detail is as follows

`y=arccos(e^(3x))`.....(i)
As
If
`y=arccosx`
Then
`y'=1/(sqrt(1-x^2))`......(ii)

Differentiating both sides of equation (i)
and using equation (ii)
`y'=1/sqrt(1-e^(6x)).e^(3x)(3)`

`y'=(3e^(3x))/sqrt(1-e^(6x))`