Cho \[f\left( x \right) = \frac{x}{{\sqrt {4 - {x^2}} }}\]. Tính\[f'\left( 0 \right)\]

Hướng dẫn giải:

Chọn A

\[f'\left( x \right) = {\left( {\frac{x}{{\sqrt {4 - {x^2}} }}} \right)^/} = \frac{{x'\sqrt {4 - {x^2}} - x{{\left( {\sqrt {4 - {x^2}} } \right)}^/}}}{{{{\left( {\sqrt {4 - {x^2}} } \right)}^2}}} = \frac{{\sqrt {4 - {x^2}} + \frac{{{x^2}}}{{\sqrt {4 - {x^2}} }}}}{{\left( {4 - {x^2}} \right)}} = \frac{4}{{\left( {4 - {x^2}} \right)\sqrt {4 - {x^2}} }}\]

Vậy \[f'\left( 0 \right) = \frac{1}{4}\].