Question

Find f '(a).
f(x) =
`(1)/(√(x) +5)`

Answer 1

`f'(a)=(1)/(2a^(3/2)+20a+50√(a))`

Explanation:

`f'(x)=((d)/(dx) (√(x)+5)(1)-(√(x)+5)(d)/(dx)(1))/((√(x)+5)^2) \\ \\ =((1)/(2√(x)))/((√(x)+5)^2) \\ \\ =((1)/(2√(x)))/(x+10√(x)+25) \\ \\ =(1)/(2x^(3/2)+20x+50√(x)) \\ \\ \therefore f'(a)=(1)/(2a^(3/2)+20a+50√(a))`