What is the derivative of #f(t) = (t^2-2e^(t-1) , t-e^t ) #?

Answer 1

Christopher Allers

#d/(d t) f(x)=(-2e^(t-1)*l n e+2t,-e^t*l n e+1)#

#f(t)=(t^2-2e^(t-1),t-e^t)#

#d/(d t)(t^2-2e^(t-1))=-2e^(t-1)*l n e+2t#

#d/(d t)(t-e^t)=-e^t*l n e+1#

#d/(d t) f(x)=(-2e^(t-1)*l n e+2t,-e^t*l n e+1)#

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Answer 2

Aurora Alvarado

To find the derivative of ( f(t) = (t^2 - 2e^{t-1}, t - e^t) ), we need to find the derivative of each component separately. The derivative of ( t^2 - 2e^{t-1} ) with respect to ( t ) is ( 2t - 2e^{t-1} ), and the derivative of ( t - e^t ) with respect to ( t ) is ( 1 - e^t ). So, the derivative of ( f(t) ) is ( (2t - 2e^{t-1}, 1 - e^t) ).

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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.