How to differentiate this [ 4 unit ] ? (1 Viewer)

Amogh · Apr 16, 2011

WolframAlpha
Click 'Show steps' in the top right of the first box

muzeikchun852 · Apr 16, 2011

Amogh said:
WolframAlpha
Click 'Show steps' in the top right of the first box

their step is very confusing. any alternative program ?

AAEldar · Apr 16, 2011

Wolfram makes it look more complicated than it is :\ I mean it's still not a simple derivative but yea >.<

We know that the $\frac{d}{dx}ln(f(x))=\frac{f'(x)}{f(x)}$ so using this you can easily differentiate $lnx$ and then put $a+\sqrt{a^2-x^2}$ on the bottom of the other denominator and differentiate that for the numerator.

kaz1 · Apr 16, 2011

this isn't 4unit lol

Amogh · Apr 16, 2011

Which steps don't you follow?

muzeikchun852 · Apr 16, 2011

AAEldar said:
Wolfram makes it look more complicated than it is :\ I mean it's still not a simple derivative but yea >.<

We know that the $\frac{d}{dx}ln(f(x))=\frac{f'(x)}{f(x)}$ so using this you can easily differentiate $lnx$ and then put $a+\sqrt{a^2-x^2}$ on the bottom of the other denominator and differentiate that for the numerator.

yep. i got all that. but i didnt get the model answer which is
as how do they jump from this line
$\frac{1}{x} + \frac{x}{\sqrt{a^2-x^2}(a+\sqrt{a^2-x^2})}$
to this
$\frac{a}{x\sqrt{a^2-x^2}}$

Drongoski · Apr 16, 2011

muzeikchun852 said:
$ln\: x - ln (a+\sqrt{a^2-x^2})$

$\frac {dy}{dx} = \frac {1}{x} - \frac {1}{a + \sqrt {a^2 - x^2}} \times \frac {1}{2} (a^2 - x^2) ^{- \frac {1}{2}} \times (-2x)$

eventually (too tedious to type out in TeX)

$= \frac {a}{x \sqrt{a^2 - x^2}}$

AAEldar · Apr 16, 2011

muzeikchun852 said:
yep. i got all that. but i didnt get the model answer which is
as how do they jump from this line
$\frac{1}{x} + \frac{x}{\sqrt{a^2-x^2}(a+\sqrt{a^2-x^2})}$
to this
$\frac{a}{x\sqrt{a^2-x^2}}$

I really have no idea. I'm staring at it and can't see anything that would make it simplify to that :\

Amogh · Apr 16, 2011

AAEldar · Apr 16, 2011

Lololol that makes sense now >.<

muzeikchun852 · Apr 16, 2011

Amogh said:
$\\ \frac{1}{x} + \frac{x}{\sqrt{a^2 - x^2} + a^2 - x^2} \\ \\ \\ \frac{x^2 + a^2 - x^2 + a\sqrt{a^2 - x^2}}{(a^2 - x^2 + a\sqrt{a^2 -x^2})x} \\ \\ \\ \frac{a(a+ \sqrt{a^2 - x^2})}{(\sqrt{a^2 - x^2})(a + \sqrt{a^2 -x^2)}x} \\ \\ \\ \frac{a}{x\sqrt{a ^2 - x^2}} \\ \\ \\$

thank you . youre a champ. + rep.

EDIT: cant rep you before i rep-ed you before.

Amogh · Apr 17, 2011

No worries

Glad I could help!

Drongoski said:
Amogh - I just love the typeface [oh no - how did it change to normal?]!

You omitted the x at the bottom.

Haha I used Texify and got that odd looking font but then figured it'd be better to stick with the default style

Riproot · Apr 17, 2011

kaz1 said:
this isn't 4unit lol

This.

How to differentiate this [ 4 unit ] ? (1 Viewer)

muzeikchun852

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