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

Explanation

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

\[ f'(x) = \frac{u'v - uv'}{v^2} \]

where \( u = x^3 \) and \( v = a^2 - x^2 \).

...