If `f(x)=log{(u(x))/(v(x))},\ u(1)=v(1)` and `u^(prime)(1)=v^(prime)(1)=2` , then find the value of `f^(prime)(1)` .

Explanation

To find the value of \( f'(1) \) given \( f(x) = \log\left(\frac{u(x)}{v(x)}\right) \), \( u(1) = v(1) \), and \( u'(1) = v'(1) = 2 \), we can follow these steps:

### Step 1: Differentiate \( f(x) \)

Using the properties of logarithms, we can differentiate \( f(x) \):

\[
f'(x) = \frac{d}{dx} \left( \log\left(\frac{u(x)}{v(x)}\right) \right)
...