Question

Find the derivative of: f(x)= sqrt(x) - 1/sqrt(x)
Please include the process.

Answer 1

remember that x^-m=1/(x^m)
first, conver to exponential

`√(x) - (1)/( √(x) ) =x^ (1)/(2)-x^ (-1)/(2)`
now do the thingummy
(1/2)(x^(-1/2))-(-1/2)(x^(-3/2))
convert to fraction form

`(1)/(2 √(x) ) + \frac{1}{2 \sqrt{x^(3)/(2)} }`

`(1)/(2 √(x) ) + (1)/(2x √(x) )`
dat is the answer

Answer 2

f(x) = x^1/2 - x^-1/2
f'(x) = 1/2*x^-1/2 - (-1/2*x^-3/2)
f'(x) = 1/2sqrt(x) + 1/2(sqrt(x))^3
f'(x) = x + 1/2(sqrt(x))^3