Derivative of a sqrt function

Can someone please tell me how to find the derivative of sqrt [2x+1/x-1] and tell me what method you used please

Good question!

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Thanks!

You the chain rule. Find the derivative of everything inside the square root radical and then multiply it by the derivative of the square root.

[(2x-2 - 2x-1) / (x-1)²] * [2x+1 / x-1] ^1/2

[(2x-2 - 2x-1) / (x-1)²] * 1/2[2x+1 / x-1] ^-1/2

[(2x-2 - 2x-1) / (x-1)²] * [ 1 / 2(2x+1/x-1)²]

Final answer:
[(2x-2 - 2x-1) / (x-1)²] * [ 1 / 2(2x+1/x-1)²]

Let u = 2x+1/x-1] & y =u^1/2
so dy/dx = dy/du * du/dx
= 1/2 u^(-1/2) * [ 2 - 1 /(x-1)^2 ]
= 1/2 [2x+1/x-1]^1/2 * [ 2 - 1 /(x-1)^2 ]

= [ 2 - 1 /(x-1)^2 ] / 2 [2x+1/x-1]^1/2