Dezembro 23, 2019

por Carleen

Como você diferencia $y = ln (1 + x ^ 2)$ ?

Responda:

$dy/dx=(2x)/(1+x^2)$

Explicação:

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.

$rArrdy/dx=1/u(2x)=(2x)/(1+x^2)$