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mathcalculus Group Title

can someone explain this simple derivative to me please: sort(6x)

  • 11 months ago
  • 11 months ago

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  1. mathcalculus Group Title
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    isn't it 1/2(6x)^(-1/2)

    • 11 months ago
  2. mathcalculus Group Title
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    how does it go from there to the answer: sqrt(6)/2 sqrt(x)

    • 11 months ago
  3. Psymon Group Title
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    It's chain rule so you also need to multiply by the derivative of the inside. So it would be what you put, but then multiply by 6.

    • 11 months ago
  4. Psymon Group Title
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    \[\sqrt{6x} = \frac{ 1 }{ 2 }(6x)^{\frac{ -1 }{ 2 }}(6)\]

    • 11 months ago
  5. mathcalculus Group Title
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    ok

    • 11 months ago
  6. mathcalculus Group Title
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    im no sure about the chain rule its confusing

    • 11 months ago
  7. mathcalculus Group Title
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    i know its: [f(g(x))]'= f'(g(x))*g'(x)

    • 11 months ago
  8. Psymon Group Title
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    Well, I have a unique way of showing it, so maybe it will help maybe not. Were you one of the ones I sent the derivative files to?

    • 11 months ago
  9. mathcalculus Group Title
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    no

    • 11 months ago
  10. mathcalculus Group Title
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    oh wait, i think so a while ago.

    • 11 months ago
  11. mathcalculus Group Title
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    let me open

    • 11 months ago
  12. Psymon Group Title
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    Ah xD Yeah, one of them had the chain rule in it. I teach it in a unique way, so maybe it helps maybe it doesn't.

    • 11 months ago
  13. mathcalculus Group Title
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    does it always work?

    • 11 months ago
  14. Psymon Group Title
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    Yeah. As long as you recognize what layers you have then yeah. Chain rule is multiplying the derivatives of each layer you have, making sure to not disturb what was originally inside of each layer.

    • 11 months ago
  15. mathcalculus Group Title
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    thanks im going to read it right now

    • 11 months ago
  16. Psymon Group Title
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    Yeah, just let me know.

    • 11 months ago
  17. mathcalculus Group Title
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    ugh i gave it a shot. wrong. :(

    • 11 months ago
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  18. Psymon Group Title
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    How'd it become 1/4?

    • 11 months ago
  19. mathcalculus Group Title
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    i did 1/2 *-1/2

    • 11 months ago
  20. Psymon Group Title
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    Well, you bring the power down and then you made the power become -1/2. You're done with that layer, now you just go to the inner layer. \[\frac{ 1 }{ 2 }(----)^{\frac{ -1 }{ 2 }}\] Thats it, no more to that part.

    • 11 months ago
  21. mathcalculus Group Title
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    huh?

    • 11 months ago
  22. Psymon Group Title
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    Well, when you do the outer layer. All you do is bring the power down as a multiplication then lower the power by 1. After that you are done with that layer. There's no other 1/2 to multiply by.

    • 11 months ago
  23. mathcalculus Group Title
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    down in the denominator?

    • 11 months ago
  24. mathcalculus Group Title
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    can you show me the steps to the answer? just want to see how you did it so i can ask

    • 11 months ago
  25. Psymon Group Title
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    Alright, so we have two layers. The first layer is simply ( )^1/2 and the inner layer 6x. So the chain rule says that we take the derivative of each layer and multiply the results. So following the normal derivative rule of \[\frac{ d }{ dx }k ^{n} = nk ^{n-1}\], I'll do that with the first layer. \[\frac{ 1 }{ 2 }(---)^{-\frac{ 1 }{ 2 }}\]I just left the inner part blank for now, but that is the derivative of the first layer. Now I do the second layer, which is just 6x. So the derivativeof 6x is simply 6. So now that I have the derivative of both layers, I now multiply both of these derivatives \[\frac{ 1 }{ 2 }(---)^{-\frac{ 1 }{ 2 }}*(6)\] This of course becomes: \[\frac{ 3 }{ (---)^{\frac{ 1 }{ 2 }}}\] Now all that is left to do is plug back in what was originally inside of that layer, giving us: \[\frac{ 3 }{ \sqrt{6x} }\]

    • 11 months ago
  26. mathcalculus Group Title
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    oh the answer is sqrt (6)/2 sqrt(x)

    • 11 months ago
  27. Psymon Group Title
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    It's the same thing actually xD

    • 11 months ago
  28. Psymon Group Title
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    I'll show ya why: \[\frac{ 3 }{ \sqrt{6x} }=\frac{ 3 }{ (\sqrt{6})(\sqrt{x)} }\]Now multiply top and bottom by sqrt(6) \[\frac{ 3(\sqrt{6)} }{ (\sqrt{6})(\sqrt{x})(\sqrt{6}) }\]This then becomes finally: \[\frac{ \sqrt{6} }{ 2\sqrt{x} }\]

    • 11 months ago
  29. mathcalculus Group Title
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    alrigght thanks ! :)))

    • 11 months ago
  30. Psymon Group Title
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    Mhm, np ^_^ Hope that made sense xD

    • 11 months ago
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