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anonymous

  • 5 years ago

Find the first derivative of f(θ)=(θ+1)cosθ

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  1. amistre64
    • 5 years ago
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    replace that theta thing with a normal looking variable for starters :)

  2. amistre64
    • 5 years ago
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    (x+1)cos(x) distribute the cos thru x cos(x) + cos(x) now derive both of them seperately

  3. amistre64
    • 5 years ago
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    Dx(x cosx) + Dx(cosx)

  4. amistre64
    • 5 years ago
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    the first term is a product, so use the product rule on it...

  5. amistre64
    • 5 years ago
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    x Dx(cosx) + Dx(x) cosx + Dx(cosx)

  6. amistre64
    • 5 years ago
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    -x sin(x) + cos(x) - sin(x)

  7. nowhereman
    • 5 years ago
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    That looks rather complicated. I would do it like this: \[Df = \cos θ D(θ+1) + (θ+1)D\cos θ = \cos θ - (θ+1)\sin θ\]

  8. anonymous
    • 5 years ago
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    could both answers be used as the correct answer?

  9. nowhereman
    • 5 years ago
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    Yes, and they yield the same result after all.

  10. amistre64
    • 5 years ago
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    Both answers are exactly the same :) I just didnt factor mine out.

  11. anonymous
    • 5 years ago
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    oh well thank you so much :)

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