Question

take derivative of (4x-5)/3(x-3)^(2/3)

Answer 1

\[4x-5\over3(x-3)^{2/3}\]is this the problem?

Answer 2

yes

Answer 3

I got (4x-5)/3(x-3)^(5/3), I got it wrong

Answer 4

you could use the quotient rule but I would prefer to convert this to a product rule problem, does it matter how you do this?

Answer 5

no

Answer 6

Then I would convert this to\[{4x-5 \over 3(x-3)^{2/3}}=(1/3)[(4x-5)(x-3)^{-2/3}]\]now let's just forget about the 1/3 and focus on the product in brackets:\[(4x-5)(x-3)^{-2/3}\]let's differentiate that...

Answer 7

\[(4x-5)(-2/3)(x-3)^{-5/3}+4(x-3)^{-2/3}\]factor out the (x-3)^(-5/3) and now let's remember to put back that 1/3 we had earlier, giving us\[=(1/3)(x-3)^{-5/3}[(-2/3)(4x-5)+4(x-3)]\]simplify what's in the brackets...

Answer 8

\[(1/3)(x-3)^{-5/3}(-8x/3+10/3+4x-12)\]\[=(1/3)(x-3)^{-5/3}(4x/3-26/3)\]factor out another 2/3 from the last set of parentheses:\[=(2/9)(x-3)^{-5/3}(2x-13)\] there are other ways to write this, but that is the answer it seems.

Answer 9

\[{4x-26 \over 9(x-3)^{5/3}}\]is another way to write it.

Answer 10

questions? comments? Just post if you have them.

Answer 11

I got all the steps thanks