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- Nov 19th 2010, 06:39 AMsoftballchickHelp on log derivation

**Moderator edit:**Restored deleted question. Thread closed. - Nov 19th 2010, 06:47 AMharish21
what have you tried?

Hint: write $\displaystyle x^3(x-2)^3 = (x(x-2))^3=(x^2-2x)^3$

so have $\displaystyle \dfrac{x^3(x-2)^3}{(x^2+8)^7} = (x^2-2x)^3\; (x^2+8)^{-7}$

use the product rule! - Nov 19th 2010, 06:48 AMTheCoffeeMachine
- Nov 19th 2010, 11:37 AMHallsofIvy
If $\displaystyle f(x)= \frac{x^3(x- 2)^3}{(x^2+ 8)^7}$

then $\displaystyle ln(f(x))= 3 ln(x)+ 3ln(x- 2)- 7 ln(x^2+ 8)$

So that $\displaystyle \frac{1}{f(x)}\frac{df}{dx}= $ the derivative on the right.

To find $\displaystyle \frac{df}{dx}$ differentiate on the right and multiply by $\displaystyle f(x)= \frac{x^3(x- 2)^3}{(x^2+ 8)^7}$. - Nov 19th 2010, 01:55 PMsoftballchick
thanks I got it!

- Nov 19th 2010, 02:04 PMTheCoffeeMachine