Question

Найдите пожалуйста производную

Answer 1

$y' = frac{x' * sqrt{3 x^{2} +1}- x* ( sqrt{3 x^{2} +1})' }{2 sqrt{3 x^{2} +1} }= frac{ sqrt{3 x^{2} +1}-x* frac{1}{2 sqrt{3 x^{2} +1} }*(3 x^{2} +1)' }{2 sqrt{3 x^{2} +1} }=$$frac{ sqrt{3 x^{2} +1}- frac{6 x^{2} }{2 sqrt{3 x^{2} +1} } }{2 sqrt{3 x^{2} +1} }= frac{2(3 x^{2} +1)-6 x^{2} }{4(3 x^{2} +1)} =$$frac{6 x^{2} +2-6 x^{2} }{4(3 x^{2} +1)} = frac{2}{4(3 x^{2} +1)} = frac{1}{2(3 x^{2} +1)}$