Задача 57801 Найдите производную dy/dx данных функций...

601cf98c2953aa67a8344bef

09.02.2021 14:48:55

Найдите производную dy/dx данных функций

5ff1d32e960c3c35933d951f

09.02.2021 16:50:03

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[m]y=\frac{2x-3}{\sqrt{x^2+4x-3}}=\frac{(2x-3)'\sqrt{x^2+4x-3}-(2x-3)(\sqrt{x^2+4x-3})'}{(\sqrt{x^2+4x-3})^2}=[/m]
[m]\frac{2\sqrt{x^2+4x-3}-(2x-3)*\frac{1}{2\sqrt{x^2+4x-3}}*(2x+4)}{x^2+4x-3}=[/m]
[m]\frac{2\sqrt{x^2+4x-3}-(2x-3)*\frac{1}{2\sqrt{x^2+4x-3}}*2(x+2)}{x^2+4x-3}=[/m]
[m]\frac{2\sqrt{x^2+4x-3}-(2x-3)*\frac{1}{\sqrt{x^2+4x-3}}*(x+2)}{x^2+4x-3}=[/m]
[m]\frac{2\sqrt{x^2+4x-3}-\frac{(2x-3)(x+2)}{\sqrt{x^2+4x-3}})}{x^2+4x-3}=[/m]
[m]\frac{2\sqrt{x^2+4x-3}-\frac{(2x-3)(x+2)}{\sqrt{x^2+4x-3}}}{x^2+4x-3}=[/m]
[m]\frac{2\sqrt{x^2+4x-3}-\frac{2x^2+x-6}{\sqrt{x^2+4x-3}}}{x^2+4x-3}=[/m]
[m]\frac{\frac{2(x^2+4x-3)-(2x^2+x-6)}{\sqrt{x^2+4x-3}}}{x^2+4x-3}=[/m]
[m]\frac{\frac{2x^2+8x-6=2x^2-x+6}{\sqrt{x^2+4x-3}}}{x^2+4x-3}=\frac{\frac{7x}{\sqrt{x^2+4x-3}}}{x^2+4x-3}=\frac{7x}{(x^2+4x-3)\sqrt{x^2+4x-3}}[/m]