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mr.luna

  • 3 years ago

when you derive for example 5ln(X^2 +2) why isnt product rule used? my buddy here says five is just a multiplier for derivative of lnf(x), why?

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  1. victorarana
    • 3 years ago
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    You can use that rule but it's not necessary.

  2. agdgdgdgwngo
    • 3 years ago
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    where would you apply the product rule here?

  3. mr.luna
    • 3 years ago
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    isnt it 5*lnf(x)

  4. agdgdgdgwngo
    • 3 years ago
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    \begin{array}l\color{#FF0000}{\text{I}}\color{#FF0000}{\text{ }}\color{#FF7F00}{\text{s}}\color{#FF7F00}{\text{ }}\color{#FFE600}{\text{n}}\color{#FFE600}{\text{ }}\color{#00FF00}{\text{'}}\color{#00FF00}{\text{ }}\color{#0000FF}{\text{t}}\color{#0000FF}{\text{ }}\color{#6600FF}{\text{ }}\color{#6600FF}{\text{ }}\color{#6600FF}{\text{t}}\color{#6600FF}{\text{ }}\color{#8B00FF}{\text{h}}\color{#8B00FF}{\text{ }}\color{#FF0000}{\text{a}}\color{#FF0000}{\text{ }}\color{#FF7F00}{\text{t}}\color{#FF7F00}{\text{ }}\color{#FFE600}{\text{ }}\color{#FFE600}{\text{ }}\color{#FFE600}{\text{t}}\color{#FFE600}{\text{ }}\color{#00FF00}{\text{h}}\color{#00FF00}{\text{ }}\color{#0000FF}{\text{e}}\color{#0000FF}{\text{ }}\color{#6600FF}{\text{ }}\color{#6600FF}{\text{ }}\color{#6600FF}{\text{c}}\color{#6600FF}{\text{ }}\color{#8B00FF}{\text{h}}\color{#8B00FF}{\text{ }}\color{#FF0000}{\text{a}}\color{#FF0000}{\text{ }}\color{#FF7F00}{\text{i}}\color{#FF7F00}{\text{ }}\color{#FFE600}{\text{n}}\color{#FFE600}{\text{ }}\color{#00FF00}{\text{ }}\color{#00FF00}{\text{ }}\color{#00FF00}{\text{r}}\color{#00FF00}{\text{ }}\color{#0000FF}{\text{u}}\color{#0000FF}{\text{ }}\color{#6600FF}{\text{l}}\color{#6600FF}{\text{ }}\color{#8B00FF}{\text{e}}\color{#8B00FF}{\text{ }}\color{#FF0000}{\text{,}}\color{#FF0000}{\text{ }}\color{#FF7F00}{\text{ }}\color{#FF7F00}{\text{ }}\color{#FF7F00}{\text{n}}\color{#FF7F00}{\text{ }}\color{#FFE600}{\text{o}}\color{#FFE600}{\text{ }}\color{#00FF00}{\text{t}}\color{#00FF00}{\text{ }}\color{#0000FF}{\text{ }}\color{#0000FF}{\text{ }}\color{#0000FF}{\text{t}}\color{#0000FF}{\text{ }}\color{#6600FF}{\text{h}}\color{#6600FF}{\text{ }}\color{#8B00FF}{\text{e}}\color{#8B00FF}{\text{ }}\color{#FF0000}{\text{ }}\color{#FF0000}{\text{ }}\color{#FF0000}{\text{p}}\color{#FF0000}{\text{ }}\color{#FF7F00}{\text{r}}\color{#FF7F00}{\text{ }}\color{#FFE600}{\text{o}}\color{#FFE600}{\text{ }}\color{#00FF00}{\text{d}}\color{#00FF00}{\text{ }}\color{#0000FF}{\text{u}}\color{#0000FF}{\text{ }}\color{#6600FF}{\text{c}}\color{#6600FF}{\text{ }}\color{#8B00FF}{\text{t}}\color{#8B00FF}{\text{ }}\color{#FF0000}{\text{ }}\color{#FF0000}{\text{ }}\color{#FF0000}{\text{r}}\color{#FF0000}{\text{ }}\color{#FF7F00}{\text{u}}\color{#FF7F00}{\text{ }}\color{#FFE600}{\text{l}}\color{#FFE600}{\text{ }}\color{#00FF00}{\text{e}}\color{#00FF00}{\text{ }}\color{#0000FF}{\text{?}}\color{#0000FF}{\text{ }}\end{array}

  5. mr.luna
    • 3 years ago
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    beats me dude

  6. victorarana
    • 3 years ago
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    You can apply that rule like this: \[\frac{d}{dt} 5\times \ln{(x^2+2)}+5\times\frac{d}{dt}\ln{(x^2+2)}\]

  7. mr.luna
    • 3 years ago
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    oh! ok. got it. they cansel.

  8. agdgdgdgwngo
    • 3 years ago
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    ...

  9. victorarana
    • 3 years ago
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    Usually it's better to use the chain rule when you have a product of two non constant functions.

  10. victorarana
    • 3 years ago
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    If you apply it to a product of a constant and a function you'll be loosing your time, but your result will be correct

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