Como você diferencia y = log x ^ 2 ?

Responda:

dy/dx=2/x

Explicação:

There are 2 possible approaches.

color(blue)"Approach 1"

differentiate using the color(blue)"chain rule"

color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(log(f(x)))=1/(f(x)).f'(x))color(white)(2/2)|)))

y=log(x^2)

rArrdy/dx=1/x^2.d/dx(x^2)=1/x^2 xx2x=2/x

color(blue)"Approach 2"

Using the color(blue)"law of logs" then differentiate.

color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx^n=nlogx)color(white)(2/2)|)))

y=logx^2=2logx

rArrdy/dx=2xx 1/x=2/x