Please help on a Calculus tangent line problem (chain rule)

I can't quite seem to get it right!

Find an equation of the tangent line to the curve at the point (1, 1/e)

y = x^4e^−x

does y = x⁴ e^-x?if yes then do the following:

find the derivative of y, get

y' = 4x³e^-x - x⁴ e^-x....................................…
or
y' = 4x³e^-x - y

next use equation 1 as the gradient of the tangent line, with x = 1 the eqn 1 become

m = y' = 4x³e^-x - x⁴ e^-x
m = 4e^-x - e^-x
m = 3e^-x
m = 3/e

next, use formula y - y₁ = m(x - x₁) to find tangent line, rearrange we get:

y - 1/e = 3/e(x - 1)
y = (3/e)x - 2/e


(solved)

y ' = (x^4) * e^(-x) ] ' = 4x^3/e^(x) - (x^4)/e^(x) = (x^3)/e^(x)(4 - x)

y' (1) = 1/e(4 - 1) = 1/3e

y - f(1) = f ' (1) (x - 1)
y - 1/e = 1/3e (x - 1)

y = (1/3e)x - 1/3e +1/e

y = (1/3e) x +(2/3e)