Help with Chain Rule problem (Multivariable Calc)

Hi there, I'm having a hard time solving this particular problem:

"Use appropriate forms of the chain rule to find the derivatives"

Let t = u/v; u = X^2 - y^2, v = 4xy^3

Find ∂t/∂x and ∂t/∂y

Now, the answer from the solutions manual is supposed to be

∂t/∂x = x^2 + y^2/4x^2y^3

∂t/∂y =y2 − 3x2/4xy4

Here's what I tried:

∂t/∂x = (2x - y^2)(4xy^3) - (x^2 - y^2)(4y^3)/ (4xy^3)^2

I couldn't come up with the right answer this way, I know I'm missing the chain rule here, according to the problem it has to be applied somewhere but I can't just figure out how. Can someone help me out with this? :)