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Do i just use the chain rule to differentiate 3^2x

  1. Jun 6, 2004 #1
    Do i just use the chain rule to differentiate 3^2x
  2. jcsd
  3. Jun 6, 2004 #2
    Is that [tex]3^{2x}[/tex]? If so, yes, you can use the chain rule, or you could write it as [tex](3^2)^x = 9^x[/tex] and differentiate that instead.
  4. Jun 6, 2004 #3
    You might not know the chain rule for forms a^u. I certainly didn't encounter it a lot. Use this:

    [tex]\frac{d}{dx}a^u = a^u(\ln a)\frac{du}{dx}[/tex]

    a is a constant. u is a function of x.
    Last edited: Jun 6, 2004
  5. Jun 6, 2004 #4


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    Or you can do the following
    [tex] y=3^{2x} => ln(y)=2x*ln(3)[/tex]
    Now differentiate both sides (note : ln(3) is just a constant) :
    [tex] \frac {d} {dx} ln(y) = log(3)*{\frac{d} {dx}} 2x = 2*ln(3)[/tex]

    But [tex] \frac {d} {dx} ln(y) =\frac{1} {y} \frac {dy} {dx} = \frac {1} {3^{2x}} \frac {dy} {dx} [/tex]

    So [tex] \frac {dy} {dx} = 3^{2x}*2ln(3)[/tex]
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