If y is a function of t, find dy/dt at t = 2. t^2 + 4y^2 = 4.

Answer 1

t^2 + 4y^2 = 4

4y^2 = 4 - t^2

y^2 = (4 - t^2)/4

y = +or- sqrt( 4 - t^2) / 2

y = +or-(1/2) sqrt( 4 - t^2)

dy/dt = +or-(1/2) (1/2) (4 - t^2)^(-1/2) (-2t)

= +or-(1/2)t / sqrt(4 - t^2)

derivative does not exist at t=2