Derivative of a sqrt function
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Derivative of a sqrt function

[From: ] [author: ] [Date: 11-06-08] [Hit: ]
Pan (TucsonMathDoc) has recorded a YouTube video to help visually answer it.Please comment on YouTube or Y!A and let her know if it helped.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.......
Can someone please tell me how to find the derivative of sqrt [2x+1/x-1] and tell me what method you used please

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Good question!

To make learning math a bit easier, Dr. Pan (TucsonMathDoc) has recorded a YouTube video to help visually answer it.

Please comment on YouTube or Y!A and let her know if it helped.

Thanks!

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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]

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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
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keywords: function,Derivative,sqrt,of,Derivative of a sqrt function
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