Results 1 to 2 of 2

Math Help - d(x^e^x)/dy'',??

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    74

    d(x^e^x)/dy'',??

    Ive never been shown the technique for this differential. Anybody know it?? thnx! diff: y=x^e^x hmm latex won't let me write this one, basicall y=x to the power exp(x)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Mathstud28's Avatar
    Joined
    Mar 2008
    From
    Pennsylvania
    Posts
    3,641

    Thumbs down

    Quote Originally Posted by oxrigby View Post
    Ive never been shown the technique for this differential. Anybody know it?? thnx! diff: y=x^e^x hmm latex won't let me write this one, basicall y=x to the power exp(x)
    If you are asking what \frac{d}{dx}\bigg[x^{e^x}\bigg] equals then I can help you. first note that

    x^{e^x}=e^{\ln\left(x^{e^x}\right)}=e^{e^x\ln(x)}

    So now knowing that \frac{d}{dx}\bigg[e^{u(x)}\bigg]=u'(x)e^{u(x)}

    And that \frac{d}{dx}\bigg[e^x\ln(x)\bigg]=e^x\ln(x)+\frac{e^x}{x}

    We can see that

    \frac{d}{dx}\bigg[e^{e^x\ln(x)}\bigg]=\left(e^x\ln(x)+\frac{e^x}{x}\right)e^{e^x\ln(x)}  =\left(e^x\ln(x)+\frac{e^x}{x}\right)x^{e^x}
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum