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#1 2005-10-25 20:27:05

KiWoonG
Guest

differentiation of log functions

Hi, I'm having problems with log functions...

how do you diffenerentiate

                  x   
          ln ---------
                  2

and...

                     4
4x^3 - ln ------------ x
                     3


Thank you.

#2 2005-10-25 21:09:38

mathsyperson
Moderator

Offline

Re: differentiation of log functions

The differential of ln f(x) is f'(x)/f(x). For a function of the form y=ln (mx), the differential will always be 1/x. So ln (x/2) differentiated is 1/x and so is ln (4x/3).

To differentiate something like ax^b, multiply by the power, then take one off the power. So, the differential of 4x would be 12x.

To recap, y = ln (x/2), dy/dx = 1/x

y = 4x - ln (4x/3), dy/dx = 12x - 1/x


Why did the vector cross the road?
It wanted to be normal.

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