Question

Suppose that x = x(t) and y = y(t) are both functions of t. If x^2 + y^2 = 25, and dx/dt = 2 when x = 3 and y = 4, what is dy/dt?

Answer 1

dy/dt = -3/2

Explanation:

x² + y² = 25

2x dx/dt + 2y dy/dt = 0

x dx/dt + y dy/dt = 0

3 * 2 + 4 dy/dt = 0

so

dy/dt = -6/4 = -3/2