The reaction to x units of a drug t hours after it was administered is given by

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The reaction to x units of a drug t hours after it was administered is given by R(x, t) = x2(a - x)t2e-t, for 0 ≤ x ≤ a (where a is a constant). Find the following.

(a) ∂R/∂x

(b) ∂R/∂t

(c) ∂2R/∂x2

(d) ∂2R/∂x∂t

(e) Interpret your answers to parts (a) and (b).

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