t rule (1 Viewer)

iStudent · Apr 22, 2014

is there a reason why textbooks all do:
$t = tan\frac{x}{2}$

$\frac{dt}{dx} = \frac{1}{2}sec^{2}\frac{x}{2}$

$\frac{dt}{dx} = \frac{1}{2}(1+tan^{2}\frac{x}{2})$

$\frac{dt}{dx} = \frac{1}{2}(1+t^{2})$

$dx = \frac{2dt}{1+t^{2}}$

instead of:

$t = tan\frac{x}{2}$

$tan^{-1}t = x/2$

$2\frac{dt}{1+t^{2}} = dx$

Which is much faster (imo). Is there something wrong with using the latter method? Or are textbooks just against using inverse trig differentiation =/

deadpatch · Apr 22, 2014

do whatever u want

braintic · Apr 23, 2014

Coroneos did it the long way years ago, and everyone has been copying them blindly since then.

iStudent · Apr 23, 2014

I see..
thanks

t rule (1 Viewer)

iStudent

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deadpatch

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braintic

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iStudent

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