# Calculus

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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)]

• Calculus -

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.

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