# How to find the derivative of a function

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• September 27th 2009, 11:41 AM
Rainy2Day
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.
• September 27th 2009, 11:57 AM
skeeter
Quote:

Originally Posted by Rainy2Day
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 ...

$f'(-1) = \lim_{x \to -1} \frac{f(x) - f(-1)}{x - (-1)}$
• September 27th 2009, 12:06 PM
Scott H
You can also use trigonometric functions.

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