How do you differentiate #(3+2x - x^2)^(1/2)#?
The expression is a function (a square root) of a function (a polynomial of order two) so the chain rule will prove useful.
This compound function might be considered one function (the inner one) wrapped up in the other function (the outer one).
Under the chain rule, the overall derivative is the derivative of the outer function, keeping the inner function as its argument, times the derivative of the inner function.
The outer function is the square root function.
Denoting this outer function, taking some arbitrary argument
this has derivative
in this particular case,
The inner function is a simple polynomial. Denoting this by
it might be noted that this has derivative
The overall derivative is the product of these two derivatives, that is,