Производные y=[latex] \frac{x^3+3}{x^2-1} [/latex] ;[latex] x_{0} [/latex]=2

Question

Производные y=[latex] \frac{x^3+3}{x^2-1} [/latex] ;[latex] x_{0} [/latex]=2

Алгебра

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Ответ(ы) на вопрос:

Accepted Answer

y' = [latex] \frac{3x^{2}(x^{2}-1)-(x^{3}+3)2x}{(x^{2}-1)^{2}} = \frac{3x^{4}-3x^{2}-2x^{4}-6x}{(x^{2}-1)^{2}} = \frac{x^{4}-3x^{2}-6x}{(x^{2}-1)^{2}}[/latex] y'(x₀) = y'(2) = [latex]\frac{2^{4}-3*2^{2}-6*2}{(2^{2}-1)^{2}} = \frac{16-12-12}{9} = - \frac{8}{9}[/latex]