[latex]y= \frac{x-4}{ \sqrt{ x^{2}-8 } } [/latex] производная

[latex]y= \frac{x-4}{ \sqrt{ x^{2} -8} } ; \\ \\ y'=(\frac{x-4}{ \sqrt{ x^{2} -8} } )'= \\ \\ = \frac{(x-4)' \sqrt{ x^{2} -8}-(x-4)( \sqrt{ x^{2} -8})' }{ (\sqrt{ x^{2} -8})^2 } = \\ \\ = \frac{ \sqrt{ x^{2} -8}- \frac{x(x-4)}{ \sqrt{ x^{2} -8} } }{ x^{2} -8} = \frac{ \frac{ 4x-8}{ \sqrt{ x^{2} -8} } }{ x^{2} -8} = \frac{4x-8}{ \sqrt{ x^{2} -8}*( x^{2} -8) } = \frac{4(x-2)}{( x^{2} -8)^{ \frac{3}{2} } } .[/latex]