How do you use the quotient rule to find the derivative of y=(1+sqrt(x))/(1-sqrt(x))y=1+√x1−√x ?

1 Answer
Gaurav
Sep 2, 2014

y'=1/(sqrtx)*1/((1-sqrtx)^2)

Explanation :

Using Quotient Rule, which is

y=f(x)/g(x), then

y'=(g(x)f'(x)-f(x)g'(x))/(g(x))^2

Similarly following for the given problem,

y=(1+sqrtx)/(1-sqrtx)

y'=((1-sqrtx)(1/(2sqrtx))-(1+sqrtx)(-1/(2sqrtx)))/((1-sqrtx)^2)

y'=1/(2sqrtx)*(1-sqrtx+1+sqrtx)/((1-sqrtx)^2)

y'=1/(2sqrtx)*(2)/((1-sqrtx)^2)

y'=1/(sqrtx)*1/((1-sqrtx)^2)

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