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**KiWoonG****Guest**

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

how do you diffenerentiate

x

ln ---------

2

and...

4

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

3

Thank you.

**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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 4x³ would be 12x².

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

y = 4x³ - ln (4x/3), dy/dx = 12x² - 1/x

Why did the vector cross the road?

It wanted to be normal.

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