Mechanism of the reaction is:
`A_(2) overset(k_(2))hArr 2A`
`A + B overset(k_(2))rarr C`
`A_(2) + C overset(k)rarr D + A`
What is `(d[D])/(dt)` ?

Explanation

To find the rate of change of concentration of D with respect to time, \(\frac{d[D]}{dt}\), we need to analyze the given reaction mechanism step by step.

### Step 1: Identify the relevant reaction
From the provided mechanism, we can see that D is produced only in the third reaction:
\[ A_2 + C \overset{k}{\rightarrow} D + A \]

### Step 2: Write the rate expression for the formation of D
The rate of formation of D from the third reaction can be expressed using the rate constant \(k\) and the concentrations of the reactants involved in that reaction. The rate of appearance of D is given by:
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