Найдите производную функции: [tex]f(x)=\sqrt{1-\sqrt{x}}+\frac{2}{\sqrt{x^2-1}}-\frac{15}{(2x^4+1)^8}[/tex]. Created by Freakazoid. algebra-ru

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Найдите производную функции:
[tex]f(x)=\sqrt{1-\sqrt{x}}+\frac{2}{\sqrt{x^2-1}}-\frac{15}{(2x^4+1)^8}[/tex]

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$f(x)=\sqrt{1-\sqrt{x}}+\frac{2}{\sqrt{x^2-1}}-\frac{15}{(2x^4+1)^8}\\\\f'(x)=\frac{1}{2\sqrt{1-\sqrt{x}}}\cdot (-\frac{1}{2\sqrt{x}})+\frac{-2\cdot \frac{1}{2\sqrt{x^2-1 }}\cdot 2x}{x^2-1}-\frac{-15\cdot 8(2x^4+1)^7\cdot 8x^3}{(2x^4+1)^{16}}=\\\\=-\frac{1}{4\sqrt{x(1-\sqrt{x})}}-\frac{2x}{\sqrt{(x^2-1)^3}}+\frac{960x^3}{(2x^4+1)^{9}}\; ;\\\\\\P.S.\quad (\frac{C}{v})'=\frac{-C\cdot v'}{v^2}\; ,\; \; \; C=const\; (C'=0)$

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