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Math Help - Pls help me with this ques?

  1. #1
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    Question Pls help me with this ques?

    Let f(x) = x^x.Give a convicing argument showing that f'(2)~ 6.773.
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    Quote Originally Posted by mathcalculushelp View Post
    Let f(x) = x^x.Give a convicing argument showing that f'(2)~ 6.773.

    The first way would be to take the derivative using logarithmic differentation.

    y=x^x \iff ln(y)=x\ln(x) Now taking the implicit derivative we get

    \frac{1}{y}y'=[1+ln(x)] \iff y'=y[1+\ln(x)]=x^x[1+\ln(x)]

    Now f'(2)=2^2[1+ln(2)]=4+4\ln(2)=....

    Or you could approximate it by using the difference quotient

    f'(2) \approx =\frac{(2+h)^{2+h}-2^4}{h}


    Now use very small values of h like h=10^{-6} or some other maybe smaller values.
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