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Math Help - trig derivs.

  1. #1
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    trig derivs.

    Find the derivative of the function below.
    y(t) = sec^6(t + 1)

    can i just get some help...this one just seems weird

    thanks
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  2. #2
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    It's just a mega-chain rule deal. I'm not sure what help there is, other than demonstrating it. Once you see it, you'll have it firmly in your mind and never trip over another one.

    y'(t) = \left(6*[sec(t+1)]^{5}\right)*\left(sec(t+1)tan(t+1)\right)*(1)

    I added the final "(1)" only to emphasize that the argument of the secant also needed some attention.

    I like to write these out in a thoretical sense. It helps build understanding of the phases of the solution.

    If z(t) = h(g(r(t))), then z'(t) = h'(g(r(t)))*g'(r(t))*r'(t).

    In your case, you have h(t) = t^6, g(t) = sec(t), and r(t) = t+1.
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  3. #3
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    that helps alot, thanks. But i notice that i need the derivative of sec right, how would i get that?


    Quote Originally Posted by TKHunny View Post
    It's just a mega-chain rule deal. I'm not sure what help there is, other than demonstrating it. Once you see it, you'll have it firmly in your mind and never trip over another one.

    y'(t) = \left(6*[sec(t+1)]^{5}\right)*\left(sec(t+1)tan(t+1)\right)*(1)

    I added the final "(1)" only to emphasize that the argument of the secant also needed some attention.

    I like to write these out in a thoretical sense. It helps build understanding of the phases of the solution.

    If z(t) = h(g(r(t))), then z'(t) = h'(g(r(t)))*g'(r(t))*r'(t).

    In your case, you have h(t) = t^6, g(t) = sec(t), and r(t) = t+1.
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  4. #4
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    Well, you can derive it from fundamental principles if you like, or you can just memorize it. You should know these two:

    \frac{d}{dx}\tan(x)\;=\;\sec^{2}(x)

    \frac{d}{dx}\sec(x)\;=\;\sec(x)\tan(x)

    Get them stuck in your head, somehow.
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