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What is the derivative of #sin(x)/[1-cos(x)]#?

Answer 1

Emma Aldridge

I would use the Quotient Rule to get:

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Answer 2

Isabella Ackerman

To find the derivative of ( \frac{\sin(x)}{1 - \cos(x)} ), you can use the quotient rule. The derivative is given by:

[ \frac{d}{dx} \left( \frac{\sin(x)}{1 - \cos(x)} \right) = \frac{(1 - \cos(x)) \cdot \cos(x) - \sin(x) \cdot (-\sin(x))}{(1 - \cos(x))^2} ]

After simplification, the expression becomes:

[ \frac{\cos(x) - (1 - \cos(x))\sin(x)}{(1 - \cos(x))^2} ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.