How do you differentiate #y=sqrt(x-1)+sqrt(x+1)#?

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Answer 1 · 2016-09-04T16:11:43

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

We will have to apply the chain rule twice to this problem.

Step 1: Determine the derivative of #y = sqrt(x - 1)#

Let #y = u^(1/2)# and #u = x - 1#

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

Step 2: Determine the derivative of #y = sqrt(x + 1)#

Let #y = u^(1/2) and #u = x+ 1#

Then #dy/dx = 1/2u^(-1/2) xx 1 = 1/(2(x + 1)^(1/2))#

Step 3: Combine the two derivatives using the sum rule

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

Hopefully this helps!