Verified answer

Using the quotient rule, we get

y' = (6*e^(6x) *x - e^(6x)) / x^2 = e^(6x) * (6x - 1) / x^2.

y'' = {[6*e^(6x) + 36x*e^(6x) - 6e^(6x)]*x^2 - 2x*(6x*e^(6x) - e^(6x))} / x^4

----> y'' = [36x^3 * e^(6x) - 12x^2 * e^(6x) - 2x*e^(6x)] / x^4

----> y'' = 2*e^(6x)*(18x^2 - 6x + 1) / x^3.

y''' = 2*[{6*e^(6x)*(18x^2-6x+1)+ e^(6x)*(36x-6)}*x^3 - 3x^2*[e^(6x)*(18x^2-6x+1)]/x^6

---> y''' = 2*e^(6x)*{[6*(18x^2 - 6x + 1) + 6(6x - 1)]*x - 3*(18x^2 - 6x + 1)} / x^4

----> y''' = 6*e^(6x)*[2x*(18x^2 - 6x + 1) + 2x*(6x - 1) - (18x^2 - 6x + 1)] / x^4

----> y''' = 6*e^(6x)*(36x^3 - 12x^2 + 2x + 12x^2 - 2x - 18x^2 + 6x - 1) / x^4

----> y''' = 6*e^(6x)*(36x^3 - 18x^2 + 6x - 1) / x^4.

I dong understand y"'?! Is this y at the power of 3 or whatever unknown?! Could you give some more details? :) I lovers math and science.

y' = (6xe^(6x)-e^(6x))/x^2