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Math Help - How to find the derivative of a function

  1. #1
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    How to find the derivative of a function

    I have to find the derivative of sqrt.(4-x^2), top half of a circle, at the point x=-1.

    My teacher won't let me use the rules of differentiation. so I can't just take the 1st derivative and plug -1 in. (I found the 1st derivative so I know the answer is 1/sqrt.3 or .5773)

    Is there any other way to find the derivative at that point? If so could you explain how to do it.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Rainy2Day View Post
    I have to find the derivative of sqrt.(4-x^2), top half of a circle, at the point x=-1.

    My teacher won't let me use the rules of differentiation. so I can't just take the 1st derivative and plug -1 in. (I found the 1st derivative so I know the answer is 1/sqrt.3 or .5773)

    Is there any other way to find the derivative at that point? If so could you explain how to do it.

    Thanks in advance.
    definition of a derivative at a point ...

    f'(-1) = \lim_{x \to -1} \frac{f(x) - f(-1)}{x - (-1)}
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  3. #3
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    You can also use trigonometric functions.

    Hint: The first step is to find the angle \theta of the point of the circle at x=-1.
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