यदि $f(x) = \sqrt{\frac{(x + 1)(x + 9)}{x + 4}}$, तो $f'\left(0\right)$ क्या है?

हल

1. 01

   $\log y = \frac{1}{2}\left[\log(x + 1) + \log(x + 9) - \log(x + 4)\right]$, इसलिए 0 पर $\frac{y'}{y} = \frac{1}{2}\left(1 + \frac{1}{9} - \frac{1}{4}\right) = \frac{31}{72}$।

2. 02

   $y(0) = \sqrt{\frac{9}{4}} = \frac{3}{2}$, इसलिए $f'(0) = \frac{3}{2} \times \frac{31}{72} = \frac{31}{48}$।