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Math Help - Derivatives Of inverse functions; Derivatives and integrals involving exponential fun

  1. #1
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    Derivatives Of inverse functions; Derivatives and integrals involving exponential fun

    Show that
    a) Y= x exp-x statisfies the equation xy'=(1-x)y
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  2. #2
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    Use product rule to get: y = xe^{-x} \ \ \Rightarrow \ \ y' = e^{-x} - xe^{-x}

    So: \text{LHS} = xy' = x \left(e^{-x} - xe^{-x}\right) = \cdots

    And: \text{RHS} = (1-x)y = (1-x)(xe^{-x}) = \cdots

    Are they equal? If so, you're done.
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    do I have to use ln?

    or what is the next step
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  4. #4
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    What do you mean? We just want to show xy' = (1-x)y.

    We've got an expression for xy' and one for (1-x)y. Show that they're equal by simplifying and you're done.
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  5. #5
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    oh I see thanks, I thinking something else?
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