# Help on log derivation

• Nov 19th 2010, 06:39 AM
softballchick
Help on log derivation

Moderator edit: Restored deleted question. Thread closed.
• Nov 19th 2010, 06:47 AM
harish21
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 AM
TheCoffeeMachine
Quote:

Originally Posted by softballchick

Are we to assume that you're required to find the derivative by logarithmic differentiation? It isn't clear!
• Nov 19th 2010, 11:37 AM
HallsofIvy
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 PM
softballchick
thanks I got it!
• Nov 19th 2010, 02:04 PM
TheCoffeeMachine
Quote:

Originally Posted by softballchick
thanks I got it!

1. Be clear as to what you mean next time so as not to waste people's time.
2. Editing out posts after getting help isn't allowed, and it's a sign of cheating.