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Math Help - Derivative

  1. #1
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    Derivative

    Derivative of the function using logs

    f(t)=e^2t_ln(t+1) and f(x)=ln(2x/x+1)
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  2. #2
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    Hello factory1o1
    Quote Originally Posted by factory1o1 View Post
    Derivative of the function using logs

    f(t)=e^2t_ln(t+1) and f(x)=ln(2x/x+1)
    I assume you mean f(t) = e^{2t}\ln(t+1)

    in which case, use the product rule to get:

    f'(t)=e^{2t}\times\frac{1}{t+1}+ 2e^{2t}\ln(t+1)

    =e^{2t}\Big(\frac{1}{t+1}+ 2\ln(t+1)\Big)

    To differentiate the second function, use the properties of logs first:

    f(x) = \ln\left(\frac{2x}{x+1}\right)

    = \ln(2)+\ln(x) -\ln(x+1)

    \Rightarrow f'(x) =\frac{1}{x}-\frac{1}{x+1}

    =\frac{1}{x(x+1)}

    Grandad
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