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Math Help - Find 1st and 2nd Derivative.

  1. #1
    Affinity
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    Find 1st and 2nd Derivative.

    Find the first derivative and then the second derivative of
    Thank you in advance!
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  2. #2
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    Quote Originally Posted by Affinity View Post
    Find the first derivative and then the second derivative of
    Thank you in advance!
    y=\frac{e^x}{x^2}

    y'=\frac{(e^x)'(x^2)-(e^x)(x^2)'}{(x^2)^2}
    y'=\frac{x^2e^x-2xe^x}{x^4}=\frac{xe^x(x-2)}{x^4}=\frac{e^x(x-2)}{x^3}

    y''=\frac{[e^x(x-2)]'(x^3)-[e^x(x-2)](x^3)'}{(x^3)^2}
    y''=\frac{[(e^x)'(x-2)+e^x(x-2)']x^3-e^x(x-2)(x^3)'}{x^6}
    y''=\frac{[e^x(x-2)+e^x]x^3-3x^2e^x(x-2)}{x^6}
    y''=\frac{e^x(x-2)x^3+x^3e^x-3x^2e^x(x-2)}{x^6}=\frac{e^x[(x-2)x^3+x^3-3x^2(x-2)]}{x^6}
    y''=\frac{e^x(x^4-2x^3+x^3-3x^3+6x^2)}{x^6}=\frac{e^x(x^4-4x^3+6x^2)}{x^6}= \frac{x^2e^x(x^2-4x+6)}{x^6}
    y''=\frac{e^x(x^2-4x+6)}{x^4}
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