Question

How do I find the derivative of `ln(sqrt(x))`?

Answer 1

`1/(2x)`

Explanation:

According to the chain rule,

`d/dx[ln(u)]=(u')/u`

Therefore,

`d/dxln(x^(1/2))=(d/dx[x^(1/2)])/x^(1/2)=(1/2x^(-1/2))/x^(1/2)=1/(2x^(1/2)x^(1/2)`

`=1/(2x)`