If `f(x)=(x^(3))/(a^(2)-x^(2))` then find the value of `f'((a)/(2))`.

Explanation

To find the derivative \( f'(\frac{a}{2}) \) for the function \( f(x) = \frac{x^3}{a^2 - x^2} \), we will use the quotient rule for differentiation. The quotient rule states that if you have a function in the form \( \frac{u}{v} \), then the derivative is given by:

\[ \frac{d}{dx} \left( \frac{u}{v} \right) = \frac{v \frac{du}{dx} - u \frac{dv}{dx}}{v^2} \]

### Step 1: Identify \( u \) and \( v \)
Here, we have:
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