How do you find the derivative of Cos^-1 (3/x)?

1 Answer
May 5, 2018

= (3/x^2)/(sqrt(1-(3/x)^2))

Explanation:

We have to know that,

(arccos(x))' = -(1)/(sqrt(1-x^2))

But in this case we have a chain rule to abide,

Where we an set u = 3/x=3x^-1

(arccos(u))'=-(1)/(sqrt(1-u^2))*u'

We now only need to find u',

u' = 3(-1*x^(-1-1))=-3x^-2=-3/x^2

We will then have,

(arccos(3/x))'=-(-3/x^2)/(sqrt(1-(3/x)^2)) = (3/x^2)/(sqrt(1-(3/x)^2))