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Question Number 207402 by MATHEMATICSAM last updated on 13/May/24

$$f\left(x\right)+2f\left(\frac{1}{x}\right)=3x.$$$$f{}^{\prime }\left(x\right)=?$$

Answered by Frix last updated on 13/May/24

$$x=t:f\left(t\right)+2f\left(\frac{1}{t}\right)=3t$$$$x=\frac{1}{t}:f\left(\frac{1}{t}\right)+2f\left(t\right)=\frac{3}{t}$$$$\Rightarrow f\left(t\right)=\frac{2}{t}-t[\wedge f\left(\frac{1}{t}\right)=2t-\frac{1}{t}]$$$$\Rightarrow f^{\prime }\left(x\right)=-\frac{2}{x^2}-1$$

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