Come si differenzia y = ln (1 + x ^ 2) ?

Come si differenzia y = ln (1 + x ^ 2) ? Risposta: dy/dx=(2x)/(1+x^2) Spiegazione: differentiate using the color(blue)”chain rule” That is color(red)(|bar(ul(color(white)(a/a)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(a/a)|)))…….. (A) color(orange)”Reminder ” color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(lnx)=1/x)color(white)(a/a)|))) let u=1+x^2rArr(du)/(dx)=2x and so y=lnurArr(dy)/(du)=1/u substitute these values into (A) changing u back to terms of x. rArrdy/dx=1/u(2x)=(2x)/(1+x^2)