Question

Помогите пожалуйста Найти производную функции функции y=xlnx/1-x^2

Answer 1

$bfdisplaystyle y=frac{xcdot ln(x)}{1-x^{2}}\\\\y' = frac{(xcdot ln(x))'(1-x^{2})-(xcdot ln(x))(1-x^{2})'}{(1-x^{2})^{2}}implies\\frac{(x'cdot ln(x) + xcdot ln(x)')(1-x^{2}) - xcdot ln(x)cdot(-2x))}{(1-x^{2})^{2}}implies\\frac{(xcdot ln(x) + xcdotfrac{1}{x})(1-x^{2}) + 2x^{2}cdot ln(x)}{(1-x^{2})^{2}}implies\\frac{(ln(x) + 1)(1-x^{2}) + 2x^{2}cdot ln(x)}{(1-x^{2})^{2}}$