Find g'(x) if g(x) = x^3e^-8x. What is the equation of the tangent line to the graph of g at
the point on the curve with x-coordinate 1?

I can get the derivative no problem. I just can't seem to get the equation of the tangent line.

If your looking for the equation of the tangent line of g(x), it IS g'(x)

however if you are looking for instantaneous slope, the equation will be constant, taking on the form

x=g'(1)

And the equation of the line it creates would be of the form

y_0-y_1=g'(1)(x_0-x_1) (you know two coordinate points, x being 1 and y being g(1))