Решебник по алгебре и начала математического анализа 10 класс Алимов Задание 850

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$$1)f(x)=\frac{e^x-e^{-x}}{x}$$

$$f^{{}^{\prime }}(x)=$$

$$=\frac{{(e^x-e^{-x})}^{{}^{\prime }}\bullet x-(e^x-e^{-x})\bullet (x{)}^{\prime }}{x^2}=$$

$$=\frac{(e^x+e^{-x})\bullet x-(e^x-e^{-x})\bullet 1}{x^2}=$$

$$=\frac{x{e}^x+x{e}^{-x}-e^x+e^{-x}}{x^2}=$$

$$=\frac{e^x(x-1)+e^{-x}(x+1)}{x^2}.$$

$$2)f(x)=\frac{2^x-{\log }_{2}x}{\ln 2\bullet x}$$

$$=\frac{2^x\bullet x\bullet {\ln }^{2}2-1-2^x\bullet \ln 2+\ln x}{{(\ln 2\bullet x)}^2}=$$

$$=\frac{2^x\bullet \ln 2\bullet (x\ln 2-1)+\ln x-1}{x^2\bullet {\ln }^{2}2}.$$