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anonymous

  • 5 years ago

If f(x)=xcosx , what does f"(x)=?

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  1. anonymous
    • 5 years ago
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    i am thinking it would be f"(x)=-cos

  2. anonymous
    • 5 years ago
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    No, you need to use the product rule for that one because you're multiplying two different expressions of x. Do you know the product rule?

  3. anonymous
    • 5 years ago
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    f(x)=(xcosx)(1-sin1)

  4. anonymous
    • 5 years ago
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    With the product rule, you take the first term and call it f(x) and then the second term and call it g(x), so we would have f(x)=x and g(x)=cosx. Then the formula for product rule is f ' (x)*g(x)+f(x)*g ' (x)

  5. anonymous
    • 5 years ago
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    So the first derivative would be 1 * cosx + x * -sinx Does that make sense?

  6. anonymous
    • 5 years ago
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    ok i think i am tracking

  7. anonymous
    • 5 years ago
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    So f ' (x)=cosx-xsinx You were needing to go to the second derivative?

  8. anonymous
    • 5 years ago
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    ok now i have to use the difference equation?

  9. anonymous
    • 5 years ago
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    For the subtraction? Those derivatives can just be taken separately.

  10. anonymous
    • 5 years ago
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    So you would take the derivative of cosx, which I'm sure you know how to do, and the derivative of -xsinx, which is the product rule again.

  11. anonymous
    • 5 years ago
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    f"(x)=sinx+1*cosx+x*sinx ?

  12. anonymous
    • 5 years ago
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    The derivative of cosx is -sinx. For the product rule, you would get -1*sinx-x*cosx So altogether it would be f '' (x) = -sinx-sinx-xcosx Or f '' (x) = -2sinx-xcosx

  13. anonymous
    • 5 years ago
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    Can you see how I got that?

  14. anonymous
    • 5 years ago
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    i am trying to work it all out as we speak

  15. anonymous
    • 5 years ago
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    Sweetness i was able to work it out and it makes more sense now thanks a ton.

  16. anonymous
    • 5 years ago
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    Not a problem.

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