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Using the chain rule: f '(x) = (2x) (3) (x^2 - 1)^2      = 6x(x^2 - 1)^2

We use the quotient rule to find dy/dt. Let u = 4t and v = (t^2 + 5). Then, u' = 4 and v' = 2t. Hence,

dy/dt = u'v - v'u / v² = 4(t^2 + 5) - 4t x 2t / (t^2 + 5)² = 20 - 4t

This question wants us to find: dh/dt. We are given: dV/dt=80π and V=4πh(h+4). The equation to use here is: dh/dt = dh/dV x dV/dt. We kn...

Since we have to differentiate a fraction, we must use the quotient rule. 

The quotient rule: If y = u/v, dy/dx = (vdu/dx - udv/dx)/v²

So we must work out each of the ter...