Question

if x^2+xy=10 then whenx=2, dy/dx=?

Answer 1

Use implicit differentiation.
In my notation , y' is dy/dx
x^2 + xy = 10
2x + y + xy' = 0
What is y when x is 2? Go back to the original and plug in 2 for x. You get 2^2 + 2y = 10, and you get y = 3. So x =2, y=3: plug that into 2x + y + xy' = 0...solve for y' and that's your answer.