How do you differentiate #ln |cosx/cosx-1| #?

1 Answer
Jul 9, 2017

#d/(dx) [ln|(cosx)/(cosx) - 1|] = color(blue)(0#

Explanation:

We're asked to find the derivative

#d/(dx) [ln|(cosx)/(cosx) - 1|]#

The value #(cosx)/(cosx) = 1#:

#d/(dx)[ln|1-1|#

#d/(dx)[ln|0|]#

The natural logarithm of #0# is #-oo#:

#d/(dx)[-oo]#

The derivative of negative infinity (a constant) is #0#:

#d/(dx) [ln|(cosx)/(cosx) - 1|] = color(blue)(0#