Question

How do you find the derivative of `y=ln(sqrt(x))`?

Answer 1

`y'=1/(2x)`

Explanation

`y=ln(sqrtx)`

differentiating with respect to `x` using Chain Rule,

`y'=1/sqrt(x)*1/2x^(-1/2)`

`y'=1/sqrt(x)*(1/(2sqrt(x)))`

`y'=1/(2x)`

Answer 2

`frac{dy}{dx}=frac{1}{2x}`

Explanation:

`y=ln(sqrt(x))=ln(x^{1/2})=1/2ln(x)`

`frac{dy}{dx}=frac{1}{2x}`