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

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

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