Question

Найти производную у' если у=ln x/ √1-х^2

Answer 1

у=ln х-1/х+1

y'=1/x+1/(x+1)^2=(x^2+3x+1)/x(x+1)

y'=1/x+1/x^2=x^2+x=(1+x)/x^2

y'=(2*sqrt(x^2+1)-2x(2x)*(1/2)/sqrt(x^2+1))/(x^2+1)=sqrt(x^2+1)/(x^2+1)^2