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