Question

How do you find the second derivative of `f(x)=x^(1/2)+x^(-1/2)`?

Answer 1

Find the first derivative, and then differentiate that result again.

`f'(x) = 1/2x^(-1/2) - 1/2x^(-3/2)`

Differentiate:

`f''(x) = -1/4x^(-3/2) + 3/4x^(-5/2)`

`f''(x) = 3/(4x^(5/2)) - 1/(4x^(3/2))`

Hopefully this helps!