Answer:
To compute the derivative of the function p(t) = (t^5)(t^3) using the product rule, we can use the formula:
(d/dt)[f(t)g(t)] = f(t)(dg/dt) + g(t)(df/dt)
where f(t) = t^5 and g(t) = t^3. Applying the formula, we get:
p'(t) = f(t)g'(t) + g(t)f'(t)
= (t^5)(3t^2) + (t^3)(5t^4) [taking derivatives of f(t) and g(t)]
= 3t^7 + 5t^7 [simplifying]
Therefore, the derivative of p(t) = (t^5)(t^3) with respect to t is p'(t) = 8t^7.