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

1 Answer
Apr 10, 2015

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))