Derivative of f ( x ) = <mrow class="MJX-TeXAtom-ORD"> <msqrt>

Lovellss

Lovellss

Answered question

2022-06-23

Derivative of f ( x ) = x 2 1 x
I have the function following:
f ( x ) = x 2 1 x
And here is what I did:
f ( x ) = x 2 1 x
= ( x 2 1 ) 1 2 x
f ( x ) = x 1 2 ( x 2 1 ) 1 2 ( 2 x ) ( x 2 1 ) 1 2 x 2
= x 2 ( x 2 1 ) 1 2 ( x 2 1 ) 1 2 x 2
And I'm pretty sure that this is wrong, and the answer book says it isn't either.
I think I messed up somewhere, or didn't do it properly.
I tried using the quotient rule. Do I need to make it into an exponent, and solve it as a chainrule?
Please help me find the steps and answer to this question. Thank you.
Or is there any other steps so it can match this?:
1 x 2 x 2 1

Answer & Explanation

Mateo Barajas

Mateo Barajas

Beginner2022-06-24Added 13 answers

f ( x ) = x 2 1 x
f ( x ) = u v
Note that u = x 2 1 , v = x and v = 1 We then note that u = x x 2 1
f ( x ) = u v u v v 2
= x 2 x 2 1 x 2 1 x 2
= x 2 x 2 1 + ( x 2 1 ) x 2 1 x 2
= x 2 x 2 1 x 2 1 x 2
= 1 x 2 x 2 1
pokoljitef2

pokoljitef2

Beginner2022-06-25Added 9 answers

All your steps are fine, but your final answer can be simplified further to match the answer in your book.
x 2 ( x 2 1 ) 1 / 2 ( x 2 1 ) 2 x 2 = x 2 x 2 1 x 2 1 x 2 = x 2 x 2 1 x 2 1 x 2 1 x 2 = 1 x 2 1 x 2 = 1 x 2 x 2 1

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