How do you find the derivative of #sqrt(x - 2)#?

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Answer 1 · 2016-06-28T01:12:04

Using the chain rule.

Write as a composition of two functions:

Let your function be #f(x)#, then #y = u^(1/2)# and #u = x - 2#.

The chain rule states #dy/dx = dy/(du) xx (du)/dx#.

Differentiating y:

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

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

#y' = 1/(2u^(1/2)#

Differentiating u:

#u' = 1x^(1 - 1)#

#u' = 1x^0#

#u' = 1#

Multiplying these two derivatives:

#dy/dx = 1 xx 1/(2u^(1/2)#

#dy/dx = 1/(2sqrt(x- 2))#

Hopefully this helps!