my first line after using the product rule would be
(2x-1)^4(-1)(4x+1)^-2(4) + (4x+1)^-1(5)(2x-1(^4(2)
= -4(2x-1)^5(4x+1)^-2 + 10(4x+1)^-1(2x-1)^4
= (2x-1)^4(4x+1)^-2[-4(2x-1) + 10(4x+1)]
= (2x-1)^4(4x+1)^-2(32x + 14)
= 2(2x-1)^4(4x+1)^-2(16x+7)
perhaps your teacher will not insist that you completely simplify it.
I expected my students to arrive at the above answer.
We are doing problems with the product and quotient rules, but I'm not sure if I'm doing them correctly.
If someone could check my answer I would really appreciate it.
The original problem was y = (2x-1)^5 * (4x+1)^-1 and I got the derivative to equal y' = [(2x-1)^4/(4x+1)]/[(2x-1)+ 10 /(4x+1)]
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