Question

Let 3z=(2w-5)^3. If dw/dt =1/3, find dz/dt when z=9

Answer 1

3z = (2w - 5)³

When z = 9, we have

27 = (2w - 5)³ → 3 = 2w - 5 → w = 4

Differentiate both sides with respect to t :

3 dz/dt = 3 (2w - 5)² dw/dt

dz/dt = (2w - 5)² dw/dt

Plug in everything you know and solve for dz/dt :

dz/dt = 3² • (1/3)

dz/dt = 3