Question

Вычислите производную данной функции:

Answer 1

$y'= (frac{x ^{3}+1 }{x} ) ^{'} = frac{( x^{3}+1)'*x-x'*( x^{3}+1) }{ x^{2} } = frac{3 x^{2}*x- x^{3}-1 }{ x^{2} } = frac{3 x^{3}- x^{3}-1 }{ x^{2} } = frac{2 x^{3}-1 }{ x^{2} } .$

$y'=( sqrt{ x^{2} +1})'= frac{1}{2 sqrt{ x^{2} +1} } *( x^{2} +1)'= frac{2x}{2 sqrt{ x^{2} +1} } = frac{x}{ sqrt{ x^{2} +1} } .$