Question

How do you find the derivative of `ln(x^(1/2))`?

Answer 1

`d/dxlnx^(1/2) = 1/(2x)`

Explanation:

Use the properties of logs: `log a^b=bloga` and the natural log derivative, `d/dxlnx=1/x`

so `d/dxlnx^(1/2) = d/dx(1/2lnx)`
`:. d/dxlnx^(1/2) = 1/2 d/dx(lnx)`
`:. d/dxlnx^(1/2) = 1/2 1/x`
`:. d/dxlnx^(1/2) = 1/(2x)`