Thank you for the opportunity to help you with your question!
The derivative of a square root is just the derivative of what is inside the square root divided by 2* the square root.
f(x) = sqrt(5x)
f`(x) = 5/2*sqrt(5x) :)
For your example:
What's inside the square root: x^2 + 5 / x + 2
Derivative of that: x^2 + 4x - 5 / (x+2)^2
[x^2+4x-5] / [2*(x+2)^2*sqrt(x^2+5/x+2)]
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