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

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

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