Question

Derivation problem.

Answer 1

\[\Large \sqrt{\frac{2x}{x-1}}\]

Answer 2

Asalam o alaikum @asnaseer bhai. :)

Answer 3

Salaam to you too saifoo! :)

just rewrite it as:\[\frac{(2x)^{1/2}}{(x-1)^{1/2}}\]and use the quotient or product rule.

see here: http://www.mathsrevision.net/alevel/pages.php?page=25

Answer 4

Can you please check where i'm going wrong?

Answer 5

will do - but for future ref if you save your images as .png format they will be a lot smaller and load quicker.

Answer 6

Alright, sure. Will try my best. Thanks.

Answer 7

your calculations up to u, u', v and v' look correct - but I cannot follow the rest - does it continue at the top right of the image?

Answer 8

Yes sir.

Answer 9

From right top.

Answer 10

you have v^2 incorrect in the denominator at the top right

Answer 11

no - sorry - ignore that - I misread....

Answer 12

\[(\sqrt{x-1})^2 = x-1\]I took it directly. Is that still wrong?

Answer 13

3rd step from top right looks wrong

Answer 14

the 1st term in the numerator in incorrect

Answer 15

Where i took LCM? Can you please correct it?

Answer 16

should be: \(\sqrt{x-1}\sqrt{x-1}\)

Answer 17

Oh! Right right!!! Thanks. Let me correct it then i'll show you!

Answer 18

ok - good luck! :)

Answer 19

Should the final answer be:
\[-\frac{\sqrt 2}{2x-1 \sqrt{x^2 - x}}\]

Answer 20

doesn't look right

Answer 21

Because after correcting the mistake we get:
\[\frac{x-1-x}{2\sqrt{x^2-x}} \times \frac{1}{x-1}\]

Answer 22

And we had sqrt 2 from the beginning of the problem.

Answer 23

in the denominator there do you mean:\[2(x-1)\sqrt{x^2-x}\]

Answer 24

YES YES! Missed that 2. Sorry.

Answer 25

then yes - I believe it is correct :)

although you can also use wolframalpha to check your result: http://www.wolframalpha.com/input/?i=d%2Fdx+sqrt%282x%2F%28x-1%29%29

Answer 26

Yes! This is something which is confusing me.
They have sqrt 2 in the denominator.

Answer 27

look near the bottom where it says:

Alternate form assuming x>0

Answer 28

remember:\[\frac{\sqrt{2}}{2}=\frac{1}{\sqrt{2}}\]

Answer 29

OMG! Perfect! Got it! Thanks a ton! :)

Answer 30

yw :)