Question

How do you differentiate `y=log x^2`?

Answer 1

`dy/dx=2/x`

Explanation:

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`