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Math Help - High order derivative problem

  1. #1
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    High order derivative problem

    I having trouble figuring this problem out:

    Find f^\prime^\prime(2) for tsin\frac{\pi}{t}

    So using the product rule, f^\prime(t)= tcos\frac{\pi}{t}+sin\frac{\pi}{t}

    Using the sum rule, f^\prime^\prime(t)=t(-sin\frac{\pi}{t})+cos\frac{\pi}{t}

    so plugging in f^\prime^\prime(2)=2(-(1))+0=-2

    Does that seem right?

    Any help is greatly appreciated!
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  2. #2
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    Quote Originally Posted by ascendancy523 View Post
    I having trouble figuring this problem out:

    Find f^\prime^\prime(2) for tsin\frac{\pi}{t}

    So using the product rule, f^\prime(t)= tcos\frac{\pi}{t}+sin\frac{\pi}{t}

    Using the sum rule, f^\prime^\prime(t)=t(-sin\frac{\pi}{t})+cos\frac{\pi}{t}

    so plugging in f^\prime^\prime(2)=2(-(1))+0=-2

    Does that seem right?

    Any help is greatly appreciated!
    You need to apply the chain rule.

    f'(t)=t\cdot\cos\frac{\pi}{t}\cdot\frac{d}{dt}\lef  t(\frac{\pi}{t}\right) + \sin\frac{\pi}{t}

    etc.

    Also, IF the first derivative were what you wrote, you (still) would have gotten the wrong second derivative; the first term would require the product and chain rules, and the second term would require the chain rule.
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  3. #3
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    Quote Originally Posted by undefined View Post
    You need to apply the chain rule.

    f'(t)=t\cdot\cos\frac{\pi}{t}\cdot\frac{d}{dt}\lef  t(\frac{\pi}{t}\right) + \sin\frac{\pi}{t}

    etc.

    Also, IF the first derivative were what you wrote, you (still) would have gotten the wrong second derivative; the first term would require the product and chain rules, and the second term would require the chain rule.
    So f'(t)=t\cdot\cos\frac{\pi}{t}\cdot\frac{-\pi}{t^2}+sin\frac{\pi}{t}?
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  4. #4
    MHF Contributor undefined's Avatar
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    Quote Originally Posted by ascendancy523 View Post
    So f'(t)=t\cdot\cos\frac{\pi}{t}\cdot\frac{-\pi}{t^2}+sin\frac{\pi}{t}?
    Yep.
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