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swin2013

  • 3 years ago

derivative?

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  1. swin2013
    • 3 years ago
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    \[\ln(\cos(w-1))\]

  2. calculusfunctions
    • 3 years ago
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    To take the derivative of the natural logarithm function, divide the derivative of the argument function by the argument function. Thus\[\frac{ d(\ln f(x)) }{ x }=\frac{ f \prime(x) }{ f(x) }\]Do you understand?

  3. swin2013
    • 3 years ago
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    so it's 1/cos(w-1) * -sin(w-1) *1?

  4. calculusfunctions
    • 3 years ago
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    Sorry, that should be dx in the first denominator.

  5. calculusfunctions
    • 3 years ago
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    YES!!

  6. calculusfunctions
    • 3 years ago
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    \[\frac{ d(\ln (\cos (w -1)) }{ dx }=\frac{ -\sin (w -1) }{ \cos (w -1) }=-\tan (w -1)\]Understand?

  7. calculusfunctions
    • 3 years ago
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    @swin2013 I asked if you understood.

  8. swin2013
    • 3 years ago
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    yes i do sorry, i was working on another problem :)

  9. calculusfunctions
    • 3 years ago
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    No worries!

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