For the equation given below, evaluate at the point (2,2)

Question

For the equation given below, evaluate at the point (2,2)

2x^(3)y-4x^2=16

y' at (2,2)=?

Answer 1

2 x^3 y - 4x^2 = 16

6x^2 y + 2x^3 y' - 8x = 0

3x^2 y + x^3 y' - 4x = 0

(2,2) :

3(2^2)(3) + (2^3) y' - 4(2) = 0

3*4*3 + 8 y' - 8 = 0

12 + 8 y' - 8 = 0

8 y' + 4 = 0

y' = -4/8 = -1/2