The point (1,3) lies on the curve in the xy-plane given by the equation f(x)g(y)=24+x+y, where f is a differentiable function of x and g is a differentiable function of y.

Question

Selected values of f, f′, g, and g′ are given below. What is the value of dy/dx at the point (1,3)?

f(1) = 4

f'(1) = -2

g(3) = 7

g'(3) =1

Answer 1

We differentiaqte this equation by x: f'(x)g(y) + f(x)g'(y)dy/dx = 1 + dy/dx

At point (1,3) we have f'(1)g(3) + f(1)g'(3)dy/dx = 1 + dy/dx; - 2·7 + 4·1·dy/dx = 1 + dy/dx; 3dy/dx = 15;

dy/dx = 5