Question

Find the derivative of (2x+1)³/(3x-2)^4.
(The (3x-2) is to the fourth power. Not sure how to type the subscript into this website format).

Answer 1

u can use the quotient rule to do this

Answer 2

you also nee to apply the chain rule during the process

Answer 3

I attempted taking the derivative of the function utilizing both of those rules and received:
-(12x^2+12x+3)(2x-8)/(3x-2)^5 but the answer doesn't appear correct to me.

Answer 4

(3x - 2)^4 * 6(2x+!)^2 - (2x+1)^3 * 12(3x-2)^3
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(3x-2)^8

Answer 5

do you agree with that for first step?

Answer 6

Yes, I agree.

Answer 7

= 6(3x-2)^3 (2x+1)^2 [ (3x - 2) - 2(2x + 1)]
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(3x-2)^8

= 6(2x+1)^2 (-x - 4)
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(3x-2)^5

Answer 8

hold on i think theres an error on first line

Answer 9

lol - the algebras a bit heavy!!

Answer 10

Oh I think I see: the ! should be a 1 on the first line. & I couldn’t agree more - I had difficulty with taking the GCF of the equation, so I ended up with the incorrect answer the first time around. Thank you so much for your help! :) I really appreciate it!

Answer 11

yw - on second look i think its correct
i think its acceptable to stop at this point - there's no need to expand any more

Answer 12

Thank you!! :)