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

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Answer 1 · 2014-09-24T03:11:54

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))#