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Math Help - Chain Rule

  1. #1
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    Chain Rule

    Let s = cos (theta). Evaluate ds/dt when theta= \frac {3pi}{2} and dtheta/dt= 5.

    I have no clue what they want me to do.
    The answer is 5
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  2. #2
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    Quote Originally Posted by Truthbetold View Post
    Let s = cos (theta). Evaluate ds/dt when theta= \frac {3pi}{2} and dtheta/dt= 5.
    Hello,

    you have:

    s=\cos(\theta) . Now derivate wrt t. Use chain rule!:

    \frac{ds}{dt}=-\sin(\theta) \cdot \frac{d \theta}{dt}

    Plug in the values you know:

    \frac{ds}{dt}=-\sin\left(\frac {3\pi}{2} \right) \cdot 5

    Since -\sin\left(\frac {3\pi}{2} \right) = 1 the result is 5.
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  3. #3
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    Quote Originally Posted by earboth View Post
    Hello,

    you have:

    s=\cos(\theta) . Now derivate wrt t. Use chain rule!:

    \frac{ds}{dt}=-\sin(\theta) \cdot \frac{d \theta}{dt}

    Plug in the values you know:

    \frac{ds}{dt}=-\sin\left(\frac {3\pi}{2} \right) \cdot 5

    Since -\sin\left(\frac {3\pi}{2} \right) = 1 the result is 5.
    Ooooooh! I see.
    It threw me off that the derivative of 3pi/2 equaled 5.
    Makes sense now.
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