What is the equation of the tangent line of #f(x) =arcsin(tanx)# at #x=pi/4#?

1 Answer
Apr 16, 2016

The graph of y = f(x) has dead end at #x = pi/4#. The function is not differentiable at #x=pi/4#..

Explanation:

A sine could be tan x, for #|tan x|<=1#.

So, #2k pi -pi/4<=x<=2k pi+pi/4, k = 0, +-1, +-2..#

From the definition of arc sin (tan x) as the angle whose sine is tan x, f(x) is not differentiable at #x = pi/4#.

Yet, at an interior point of any straight piece of this series of broken graphs, the derivative is 1.

The given equation is the combined equation for

y = x,

#2k pi -pi/4<=x<=2k pi+pi/4, k = 0, +-1, +-2...#