Question

9x^2-y^2=1

Answer 1

9x^2 - y^2 = 1

a.) 18x - 2y dy/dx = 0
2y dy/dx = 18x
dy/dx = 9x/y

b.) y^2 = 9x^2 - 1
y = √(9x^2 - 1)
y' = 9x / √(9x^2 - 1)

c.) substituting y = √(9x^2 - 1) into solution for part a gives
dy/dx = 9x / √(9x^2 - 1)
Thus the two solutions are consistent.