Find the slope of line tangent to a curve (calculus)?

Question

The slope of the line tangent to the curve y^2 + (xy + 1)^3 = 0 at (2 , -1) is ...

a. -3/2
b. -3/4
c. 0
d. 3/4
e. 3/2

Use implicit differentiation.

Answer 1

derive implicitly
2y*y´+3(xy+1)^2 *(y+xy´)=0
at (2,-1)
-2y´+3(-2+1)^2*(-1+2y´)=0
-2y´-3+6y´=0
so y´= 3/4