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    why can't i use dy/dx = a^xln(a) to differentiate y=x^x?

    thank you
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    (Original post by ae86_trueno)
    why can't i use dy/dx = a^xln(a) to differentiate y=x^x?

    thank you
    x^x = e^{x \log{x}}
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    If you ln both sides you get lny=xlnx. To differentiate this you use product rule for the RHS
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    (Original post by ae86_trueno)
    why can't i use dy/dx = a^xln(a) to differentiate y=x^x?

    thank you
    The reason the result you want to use doesn't work is because it assumes that  a is just a constant number. In  x^x this is no longer true, so you don't expect the previous formula to hold.
    As you correctly pointed out however, one way to approach this problem is to review how to differentiate  y = a^x and see if you can modify the method to get the derivative of  x^x
 
 
 
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