What is the derivative of #f(t) = (t^2+1 , e^(-t^2-t) ) #?
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To find the derivative of ( f(t) = (t^2+1, e^{-t^2-t}) ), differentiate each component of the function separately with respect to ( t ).
The derivative of ( t^2 + 1 ) with respect to ( t ) is ( 2t ).
The derivative of ( e^{-t^2-t} ) with respect to ( t ) can be found using the chain rule, which gives ( (-2t - 1)e^{-t^2-t} ).
So, the derivative of ( f(t) ) is ( f'(t) = (2t, (-2t - 1)e^{-t^2-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.
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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