If x^2 + 2xy - 8 = 0, then when x = 4, dy/dx =

A. - 3/2

B. - 5/4

C. 1/2

D. 3/2

E. - 3/4

The correct answer is E, hope I am right!

For simplicity, dy/dx means f' (x);

We have y = (8 - x^2) / 2x;

Then, y = 4/x - x/2;

So, f' (x) = (4/x - x/2) ' = (4/x) ' - (x/2) ' = - 4 / (x^2) - 1/2 because we use d ifferentiation formulas, such as : (f+g) ' = f' + g'; (cf) ' = cf'; x'=1; (1/x) ' = - 1 / (x^2);

Finally, f' (4) = - 4/16 - 1/2 = - 4/16 - 8/16 = - 12/16 = - 3/4.

The correct answer is E.