Question

$y= frac{x-4}{ sqrt{ x^{2}-8 } }$ производная

Answer 1

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