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bmelyk Group Title

does y' of ln(4^s) = 1/4^s or s/4 ??

  • one year ago
  • one year ago

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  1. CliffSedge Group Title
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    \(\large ln(4^s) = s \cdot ln(4)\)

    • one year ago
  2. bmelyk Group Title
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    so it would be s/4 then.

    • one year ago
  3. CliffSedge Group Title
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    ln(4) is a constant

    • one year ago
  4. bmelyk Group Title
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    yes but the derivative of ln=1/x

    • one year ago
  5. CliffSedge Group Title
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    If you are finding \(\large y'=\frac{d}{ds}[ ln(4^s)]\) \(\large y'=\frac{d}{ds}[ ln(4)s] =\frac{d}{ds}[c\cdot s], \space c=ln(4)\)

    • one year ago
  6. CliffSedge Group Title
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    The derivative of ln x is 1/x, but ln 4 is a constant, and the derivative of a constant is zero.

    • one year ago
  7. CliffSedge Group Title
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    But here you are taking the derivative of a constant times a variable.

    • one year ago
  8. bmelyk Group Title
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    what is c*s ???

    • one year ago
  9. bmelyk Group Title
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    im confused by your explanation.

    • one year ago
  10. TuringTest Group Title
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    the derivative is with respect to s what is d/ds(s) ?

    • one year ago
  11. bmelyk Group Title
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    umm s'?

    • one year ago
  12. TuringTest Group Title
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    no, what is d/dx(x) ?

    • one year ago
  13. CliffSedge Group Title
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    s' would be if s was a function of some other variable.

    • one year ago
  14. bmelyk Group Title
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    =1

    • one year ago
  15. TuringTest Group Title
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    yes, so we just changed the name of s to x ...so d/ds(s)=?

    • one year ago
  16. bmelyk Group Title
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    =1 !

    • one year ago
  17. TuringTest Group Title
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    yes :) now what if we multiply by a constant that we call 'c' ? then d/ds(cs)=?

    • one year ago
  18. bmelyk Group Title
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    c

    • one year ago
  19. TuringTest Group Title
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    yes now for your problem we can write ln(4^s)=s*ln4 ln4 is a constant, so d/ds(ln(4^s))=?

    • one year ago
  20. bmelyk Group Title
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    ln4?

    • one year ago
  21. TuringTest Group Title
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    yes

    • one year ago
  22. bmelyk Group Title
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    so thats the answer?

    • one year ago
  23. TuringTest Group Title
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    yep

    • one year ago
  24. CliffSedge Group Title
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    Thanks for the backup, Turing!

    • one year ago
  25. TuringTest Group Title
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    No prob!

    • one year ago
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