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

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To find the derivative of the given function ( f(t) = (t - \ln(t), t^2 \sin(t)) ), we differentiate each component separately with respect to ( t ).

The derivative of the first component ( t - \ln(t) ) with respect to ( t ) is ( 1 - \frac{1}{t} ), and the derivative of the second component ( t^2 \sin(t) ) with respect to ( t ) is ( 2t \sin(t) + t^2 \cos(t) ).

Therefore, the derivative of ( f(t) ) is ( f'(t) = \left(1 - \frac{1}{t}, 2t \sin(t) + t^2 \cos(t)\right) ).

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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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- How do you transform parametric equations into Cartesian form: x= 3 + 2 cost and y= 1 + 5sint?

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