Question

How do you use the first and second derivatives to sketch `F(x) = ln(x) / sqrt(x)`?

Answer 1

`F'(x)=(2-ln(x))/(2x^(3/2))`

Explanation:

`F'(x)=(1/x*sqrt(x)-ln(x)*1/2*x^(-1/2))/x`
Multiplying numerator and denominator by `sqrt(x)`
`F'(x)=(x*1/x-ln(x)/2)/(x^(3/2))`
And doing the same with `2`
`F'(x)=(2-ln(x))/(2x^(3/2))`