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

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Answer 1 · 2017-07-09T23:28:56

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

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#