# What is the derivative of #f(t) = (tsint , t^2-tcost ) #?

Use product rule.

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The derivative of ( f(t) = (t \sin(t), t^2 - t \cos(t)) ) with respect to ( t ) is given by ( f'(t) = (\frac{d}{dt}(t \sin(t)), \frac{d}{dt}(t^2 - t \cos(t))) ). You can find the derivatives of each component function separately using the product rule and chain rule as necessary.

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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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