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anonymous

  • one year ago

What rules of derivatives and method do you use to work out the derivative to f[x]=2^x ?

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  1. anonymous
    • one year ago
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    I just realized in a whole chapter on derivatives, they never covered this one

  2. UsukiDoll
    • one year ago
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    there's a rule \[\frac{d}{dx} a^x = a^x \cdot \ln a \]

  3. UsukiDoll
    • one year ago
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    The derivative of an exponential function with base a is equal to the natural logarithm of that base times the exponential function.

  4. UsukiDoll
    • one year ago
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    so just a = 2 and plug it into that exponential rule

  5. anonymous
    • one year ago
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    thanks usuki.. is something to do with the change of base formula?

  6. UsukiDoll
    • one year ago
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    ?! it's just another derivative rule. In Calculus II THERE ARE LOTS OF THEM!

  7. anonymous
    • one year ago
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    lol, oh so there are more coming than just the good ol chain rule.

  8. UsukiDoll
    • one year ago
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    oh yeah .

  9. ganeshie8
    • one year ago
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    \[\large f(x)=2^x = e^{\ln 2^x} = e^{x*\ln 2}\] you may use the good ol chain rule now

  10. anonymous
    • one year ago
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    :) where there is a will

  11. UsukiDoll
    • one year ago
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    ewwwwww I prefer the earlier version.. much faster.

  12. ganeshie8
    • one year ago
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    both are same

  13. anonymous
    • one year ago
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    you got my vote, but that is definitely an enlightening idea for someone at my stage of learning

  14. UsukiDoll
    • one year ago
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    \[\frac{d}{dx} a^x = a^x \cdot \ln a \] ftw kthxbai!

  15. ganeshie8
    • one year ago
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    are you suggesting to memorize a new formula

  16. UsukiDoll
    • one year ago
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    what's wrong with that? it's easier and straight to the point

  17. ganeshie8
    • one year ago
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    there is nothing wrong with that its only that i felt the op wants to work it out using chain rule

  18. anonymous
    • one year ago
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    I fully appreciate both perspectives here. exploring how we come up with the rule helps me as this road twists and turns.

  19. anonymous
    • one year ago
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    and of course, just having the rule is the kind of practical approach that gets cuts through this experience with no bs, gotta love that.

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