Question

compute the derivative without using a calculator
f(x)=cos^(-1)(x) x=0.25

Answer 1

use the chain rule to find the derivative
so the derivative of the inside times the derivative of the outside
derivative of cos(x) is -sinx
then for the outside consider it as a^-1 where a=cos(x)
so in the end you get (-1)a^(-2)*(-sinx)
which is (-1)(cos(x))^(-2)*(-sinx)
which simplifies to
sin(x)
-------
(cos(x))^2

then you can just evaluate it using the unit circle and your trig stuff at x=1/4

Answer 2

hope that makes some sense, sorry if I explained it in a confusing way lol

Answer 3

i thought you would have to use the inverse derivative?