Question

What is the equation of the tangent line of `f(x) =sqrt(ln(cosx))` at `x = pi/4`?

Answer 1

This function does not exist anywhere. There is no tangent line.

Explanation:

For the function `y=cosx`, its range is `-1lt=ylt=1`. These values are then plugged into `ln(x)`. For `0ltxlt=1`, we see that `ln(x)<0`. At `x<0`, `ln(x)` is undefined.

So for this function, we have `sqrtx` when `x<0`, which does not exist. This is an impossible function unless it looked like `sqrtabs(ln(abscos(x)))`.