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Math Help - Differentiation

  1. #1
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    Unhappy Differentiation

    If 5f(x)+3f(1/x)=x+2
    y=xf(x), then dy/dx,at x=1 is ---
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  2. #2
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    Quote Originally Posted by matsci0000 View Post
    If 5f(x)+3f(1/x)=x+2
    y=xf(x), then dy/dx,at x=1 is ---

    \frac{dy}{dx}=f(x)+xf'(x)\Longrightarrow \frac{dy}{dx}(1)=f(1)+f'(1).

    From 5f(x)+3f\left(\frac{1}{x}\right)=x+2 get:

    ** x=1\Longrightarrow 5f(1)+3f(1)=1+2 and from here you get f(1)

    ** Derivating, 5f'(x)-\frac{3}{x^2}f'\left(\frac{1}{x}\right)=1 and substituing x=1 you get f'(1).

    Deduce now the solution.

    Tonio
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