SOLUTION: Hello, Would someone be able to show me how to use the quotient rule to differentiate y=sqrt(X)/(1+sqrt(x)). I've been working at this for days and cannot get to the sam

Question 943730: Hello,
Would someone be able to show me how to use the quotient rule to differentiate
y=sqrt(X)/(1+sqrt(x)).
I've been working at this for days and cannot get to the same answer as in the text book.
Thanks,
G
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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)

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