Help with Derivatives

  1. My friend asked for some help with derviatives, I said I would explain here then link him

    Here is how you do it

    [tex] \frac {d}{dx} log_b(x) = \frac {1}{xlnb} [/tex]
     
  2. jcsd
  3. so you have at first
    [tex] \frac {d}{dx} log_{10}(10/x) = \frac {1}{\frac{10}{x}ln10} [/tex]

    which simplifies to

    [tex] \frac {x}{10ln(10} [/tex]

    now you may think your done, but you need to remember the chain rule so you have

    [tex] \frac {x}{10ln(10} + \frac {d}{dx} \frac {10}{x}[/tex]

    so lets take the quotient rule and solve for [tex] \frac {10}{x}[/tex]

    f(x) = 10 f'(x)=0
    g(x) = x g'(x)=1

    g(x)f'(x)-f(x)g'(x)
    ----------------
    g(x)^2

    x*0-10*1
    ---------
    x^2

    =
    [tex] \frac {-10}{x^2} [/tex]

    so then muliply

    [tex] \frac {x}{10ln(10)} * \frac {-10}{x^2} [/tex]

    and you will get

    [tex]\frac {d}{dx} log_{10}(10/x)= \frac {-1}{ln(10)*x} [/tex]
     
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