# How do you find the derivative of #s=tsint#?

This will require the product rule for derivatives.

Recall that the product rule states that given a function that is the product of two other functions,

its derivative is

For this expression,

So,

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To find the derivative of ( s = t \sin(t) ), you can use the product rule:

[ \frac{d}{dt}(t \sin(t)) = t \frac{d}{dt}(\sin(t)) + \sin(t) \frac{d}{dt}(t) ]

Differentiating ( \sin(t) ) with respect to ( t ) yields ( \cos(t) ).

Differentiating ( t ) with respect to ( t ) yields ( 1 ).

So, ( \frac{d}{dt}(t \sin(t)) = t \cos(t) + \sin(t) ).

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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.

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.

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.

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