How do you find the derivative of #y =sqrt(x-1)#?

1 Answer
Sep 24, 2014

In this problem we have to use the Power Rule and the Chain Rule.

We begin by converting the radical(square root) to it exponential form.

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

Apply the Chain Rule

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

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

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

Convert negative exponents to positive exponents

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

Convert positive exponent to radical form

#y'=1/(2sqrt(x-1))#