xixi743
  • xixi743
What is the derivative of f(x) = ln(e^2x)?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
if you know the rules of logarithms you can see that this can be reduced to: \[f(x)=2xln(e)=\ln(e ^{2x})\] and the you should also know that the natural log is the compositional inverse function of the e^x. this means that ln(e) = 1
xixi743
  • xixi743
I understood the first step where you pulled the exponent down in front, but I'm not sure about the next part.
anonymous
  • anonymous
since the log and the exponential are inverses, that means \[\ln(e^{\text{whatever}})=\text{whatever}\]

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anonymous
  • anonymous
so you are in fact just looking at \[f(x)=2x\] and the derivative is real easy
xixi743
  • xixi743
so the ln cancels out the e and simply 2x is left?

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