y = log7(x^2 - 6x - 2)
this is base seven
is the answer 2x-6/(x^2-6x-2)
From you answer, it looks like you are looking for the derivative of
log7(x^2 - 6x - 2) even though it wasn't specified.
Since
log7(x^2 - 6x - 2)
=ln(x^2 - 6x - 2) / ln(7)
we can find the derivative of the latter instead.
Your answer would be correct if the base of the logarithm were e (natural log). In the case of base 7, you only have to divide the result by ln(7), and treat the original expression as base e.
I.e.
y = log7(x^2 - 6x - 2)
=ln(x^2 - 6x - 2) / ln(7)
dy/dx = 2x-6/(x^2-6x-2)/ln(7)