Question 1184926
If the total cost is given by the function {{{C(x) = 853 + 14sqrt(x)}}} for manufacturing {{{x}}} suits, then average cost per item is given by

{{{A(x) = (853 + 14sqrt(x))/x}}}.


===> {{{dA(x)/dx = (x*( 7/sqrt(x)) - (853 + 14sqrt(x))*1)/x^2 = (7sqrt(x) - 853 - 14sqrt(x))/x^2 = (-853 - 7sqrt(x))/x^2}}}, by direct use of the quotient rule.


Note:   You can also consider the same function {{{A(x) = 853/x + 14/sqrt(x))}}} and then differentiating termwise.