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f(x)=3xsupra xpatrat+1 cat face f(x)derivat?

Răspuns :

Veronica0
[tex]( \frac{3x}{x^2+1} )'= 3* \frac{x'(x^2+1)-(x^2+1)'x}{(x^2+1)^2} =3* \frac{x^2+1-2x^2}{(x^2+1)^2} =3* \frac{1-x^2}{(x^2+1)^2} [/tex]
[tex]F(x)= \frac{3x}{ x^{2}+1 } \\ f'(x)=(\frac{3x}{ x^{2}+1 } )'= \frac{(3x)'* (x^{2} +1)-3x*( x^{2} +1)'}{( x^{2} +1)^2}=\frac{3( x^{2} +1)-3x*2x}{( x^{2} +1)^2}= \\ =\frac{3 x^{2} +3-6 x^{2} }{( x^{2} +1)^2}=\frac{3-3 x^{2} }{(x^{2} +1)^2}=\frac{3(1-x^{2}) }{(x^{2} +1)^2}[/tex]

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