Question

y = (6x^2-6)^4/x
I would appreciate it more if work was shown. Thank you (I have the answer but want to know how to do it)

Answer 1

several ways

expand and divide:

6/x * (x^2-1)^4
= 6/x (x^8 - 6x^6 + 4x^4 - 6x^2 + 1)
6(x^7 - 6x^5 + 4x^3 - 6x + 1/x)
now take derivative:
6(7x^6 - 30x^4 + 12x^2 - 6 - 1/x^2)

quotient rule:

6(4)(x^2-1)^3(2x)(x) - 6(x^2-1)^4(1)
-----------------------------------
x^2

product rule:

6(x^2-1)^4 * 1/x
24(x^2-1)^3(2x)(1/x) + 6(x^2-1)^4(-1/x^2)

I'll let you verify that they are all the same

also, there's always wolframalpha.com:

1296 (x^2-1)^3 (7x^2+1)/x^2