calcule la derive de: g(x)= arctan(((x−1)/(2x−3)))


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Question Number 197036 by SANOGO last updated on 06/Sep/23

$c a l c u l e l a d e r i v e d e :$ $g (x) = a r c t a n (\frac{x - 1}{2 x - 3})$
	Answered by som(math1967) last updated on 06/Sep/23

	$g^{^{'}} (x) = \frac{1}{1 + {(\frac{x - 1}{2 x - 3})}^{2}} \times \frac{d}{d x} (\frac{x - 1}{2 x - 3})$ $= \frac{{(2 x - 3)}^{2}}{{(2 x - 3)}^{2} + {(x - 1)}^{2}} \times \frac{(2 x - 3) - 2 (x - 1)}{{(2 x - 3)}^{2}}$ $= \frac{- 1}{5 x^{2} - 14 x + 10}$
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