Question

find the slopes of the curve y^4=y^2-x^2 at
(sqrt(3)/4,-1/2) and (-sqrt(3)/4,1/2)

Answer 1

take the derivative and toss in your x and y values to determine slope as usual

Answer 2

D( y^4=y^2-x^2 )

4y^3 y' =2y y' -2x x'

2y^3 y' =y y' -x x'

and since x' is just dx/dx = 1


2y^3 y' =y y' -x

algebra the y' all by itself and fill in the given point values for x and y