यदि $f(x) = \frac{(x + 1)(x + 2)}{(x + 3)(x + 4)}$, तो $f'\left(0\right)$ क्या है?

हल

1. 01

   $\log y = \log(x + 1) + \log(x + 2) - \log(x + 3) - \log(x + 4)$, इसलिए 0 पर $\frac{y'}{y} = 1 + \frac{1}{2} - \frac{1}{3} - \frac{1}{4} = \frac{11}{12}$।

2. 02

   $y(0) = \frac{2}{12} = \frac{1}{6}$, इसलिए $f'(0) = \frac{1}{6} \times \frac{11}{12} = \frac{11}{72}$।