Question

Derivar a função definida por g(x)=2x/(x2-1)

Answer 1

$\mathsf{g(x)=\dfrac{2x}{x^2-1}}\\\mathsf{g'(x)=\dfrac{2(x^2-1)-2x.2x}{(x^2-1)^2}}\\\mathsf{g'(x)=\dfrac{2x^2-2-4x^2}{(x^2-1)^2}}$

$\large\boxed{\boxed{\boxed{\boxed{\mathsf{g'(x)=-\dfrac{2x^2+2}{(x^2-1)^2}}}}}}$

Answer 2

Oie, Td Bom?!

$g(x) = \frac{2x}{x {}^{2} - 1 }$

$g'(x) = \frac{d}{dx} ( \frac{2x}{x {}^{2} - 1 } )$

$g'(x) = \frac{ \frac{d}{dx} (2x) \: . \: (x {}^{2} - 1) - 2x \: . \: \frac{d}{dx} (x {}^{2} - 1)}{(x {}^{2} - 1) {}^{2} }$

$g'(x) = \frac{2(x {}^{2} - 1) - 2x \: . \: 2x}{(x {}^{2} - 1) {}^{2} }$

$g'(x) = \frac{2x {}^{2} - 2 - 4x {}^{2} }{(x {}^{2} - 1) {}^{2} }$

$g'(x) = \frac{ - 2x {}^{2} - 2 }{(x {}^{2} - 1) {}^{2} }$

$g'(x) = - \frac{2x {}^{2} + 2}{(x {}^{2} - 1) {}^{2} }$

Att. Makaveli1996