# How do you use the quotient rule to find the derivative of #y=(x-sqrt(x))/(x^(1/3))# ?

##### 1 Answer

Sep 8, 2014

#y'=2/3*1/x^(1/3)-1/6*1/x^(5/6)#

Solution:

#y=(x−sqrtx)/x^(1/3)#

#y=x/x^(1/3)-x^(1/2)/x^(1/3)#

#y=x^(2/3)-x^(1/6)# differentiating with respect to

#x# ,

#y'=2/3x^(2/3-1)-1/6x^(1/6-1)#

#y'=2/3x^(-1/3)-1/6x^(-5/6)#

#y'=2/3*1/x^(1/3)-1/6*1/x^(5/6)#