Question

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

Answer 1

the correct answer is E, hope I am right!

Answer 2

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 differentiation 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.