The volume, V, of water in a tank at time t seconds is given by V = 1/3*t^6 - 2*t^4 + 3*t^2, for t=>0. (i) Find dV/dt
The differential of a function is is rate of range of that function. Therefore to find dV/dt, we are finding the rate of change of the volume per unit time.Recall, in order to differentiate a term, e.g. xa1) First multilply the term by the power, axa2) Then reduce the power by one, to a-1, axa-1d/dx(xa) = axa-1 <--- summary of processNow we just need to apply this rule individually to each of our terms.First term therefore becomes:1/3t6 --> 6/3t6 --> 2t5Eventually you will get the answer by following this with the other terms:dV/dt = 2t5 - 8t3 + 6t
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