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Mathematics 18 Online
OpenStudy (anonymous):

derivative?

OpenStudy (anonymous):

\[\ln(\cos(w-1))\]

OpenStudy (calculusfunctions):

To take the derivative of the natural logarithm function, divide the derivative of the argument function by the argument function. Thus\[\frac{ d(\ln f(x)) }{ x }=\frac{ f \prime(x) }{ f(x) }\]Do you understand?

OpenStudy (anonymous):

so it's 1/cos(w-1) * -sin(w-1) *1?

OpenStudy (calculusfunctions):

Sorry, that should be dx in the first denominator.

OpenStudy (calculusfunctions):

YES!!

OpenStudy (calculusfunctions):

\[\frac{ d(\ln (\cos (w -1)) }{ dx }=\frac{ -\sin (w -1) }{ \cos (w -1) }=-\tan (w -1)\]Understand?

OpenStudy (calculusfunctions):

@swin2013 I asked if you understood.

OpenStudy (anonymous):

yes i do sorry, i was working on another problem :)

OpenStudy (calculusfunctions):

No worries!

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