The point (−2,4) lies on the curve in the xy-plane given by the equation f(x)g(y)=17−x−y, where f is a differentiable function of x and g is a differentiable function of y. What is the value of dy/dx at the point (−2,4) ?

We are given:
f (-2) = 3
f '(-2) = 4
g (4) = 5
g '(4) = 2