Given the curve whose equation is $xy^4 + x^3y = -6$:

1. Write an equation for $\frac { d y } { d x }$.

   Step (a):

   $y^4+4xy^3y^\prime+3x^2y+x^3y^\prime=0$

2. What is the slope of the curve at $(2, –1)$?

   Hint (b):

   Evaluate your equation in part (a) for $x = 2$, $y = -1$