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Math Help - Simplifying

  1. #1
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    Simplifying

    I need to evaluate the derivative of the function f(t)=t/cos(t) at the point (pi/3, 2pi/3). I know that I have to find the derivative of the function and then plug pi/3 into the derivative. I did that I just don't know how to simplify my answer.

    I found the derivative to be f'(x)=(sec t)(t tan t + 1)
    Please help
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  2. #2
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    Quote Originally Posted by rawkstar View Post
    I need to evaluate the derivative of the function f(t)=t/cos(t) at the point (pi/3, 2pi/3). I know that I have to find the derivative of the function and then plug pi/3 into the derivative. I did that I just don't know how to simplify my answer.

    I found the derivative to be f'(x)=(sec t)(t tan t + 1)
    Please help

    Oh dear: some messy-looking way to put the derivative. Won't it be easier to visualize writing \frac{\cos t+t\sin t}{\cos^2t}=\frac{1}{\cos t}+t\tan t\,\frac{1}{\cos t}?

    Anyway, as \cos \frac{\pi}{3}=\frac{1}{2}\,,\,\,\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2} , just plug in and evaluate.

    Tonio
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  3. #3
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    Hello rawkstar
    Quote Originally Posted by rawkstar View Post
    I need to evaluate the derivative of the function f(t)=t/cos(t) at the point (pi/3, 2pi/3). I know that I have to find the derivative of the function and then plug pi/3 into the derivative. I did that I just don't know how to simplify my answer.

    I found the derivative to be f'(x)=(sec t)(t tan t + 1)
    Please help
    f(t) = \frac{t}{\cos t}

    Using the quotient rule:

    \Rightarrow f'(t) = \frac{\cos t + t\sin t}{\cos^2t}, which agrees with your answer

    \Rightarrow f'(\tfrac{\pi}{3})=\frac{\frac12+\frac{\pi}{3}\fra  c{\sqrt3}{2}}{\frac14}

    =2+\frac{2\sqrt3\pi}{3}, which won't simplify any more unless you don't mind an irrational denominator, in which case you could write is as
    2 + \frac{2\pi}{\sqrt3}

    Grandad
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