If f is the focal length of a convex lens and an object is placed at a distance p from the lens, then its image will be at a distance q from the lens, where f, p, and q are related by the lens equation

Question

1f=1p+1q
What is the rate of change of p with respect to q if q=4 and f=2? (Make sure you have the correct sign for the rate.)

Answer 1

1/f = 1/p + 1/q
0 = -1/p^2 dp/dq - 1/q^2
dp/dq = -p^2/q^2