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

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The derivative of ( f(t) = (t + e^t, e^t - t\cos{t}) ) with respect to ( t ) is:

[ f'(t) = \left(1 + e^t, e^t - \cos{t} + t\sin{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.

- What is the derivative of #f(t) = (tlnt, 3t^2-t ) #?
- What is the arc length of the curve given by #r(t)= (1/t,1,t)# on # t in [0, 1]#?
- What is the arc length of the curve given by #r(t)= (9sqrt(2),e^(9t),e^(-9t))# on # t in [3,4]#?
- How do you differentiate the following parametric equation: # (t-t^3,3/t^4-t^3)#?
- A soccer ball kicked at the goal travels in a path given by the parametric equations: x=50t; #y=-16t^2+32t#, At what two times will the ball be at a height of 6ft.?

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