Question 943730
the quotient rule states that
Let f and g be differentiable at x with g(x)not=0. Then f/g is differentiable at x and
derivative of (f(x)/g(x))=g(x)f'(x)−f(x)g'(x) / [g(x)]^2
let f(x)=x^(1/2) and g(x)=(1+x^(1/2))
f'(x) = 1/(2*x^(1/2))
g'(x) = 1/(2*x^(1/2))
g(x)^2=(1+x^(1/2))^2 
we can solve the expression
derivative of (f(x)/g(x)) = (1+x^(1/2))*1/(2*x^(1/2)) - (x^(1/2))*1/(2*x^(1/2)) / (1+x^(1/2))^2 
derivative of (f(x)/g(x)) = ( (1+x^(1/2) - (x^(1/2) ) / (2*x^(1/2) ) / (1+x^(1/2))^2 
derivative of (f(x)/g(x)) = 1 / (2*(1+x^(1/2))^2)*x^(1/2)