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