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

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The derivative of ( f(t) = (t - \sin t, \frac{\cos t}{t^2}) ) with respect to ( t ) is:

[ f'(t) = \left(1 - \cos t, -\frac{\sin t}{t^2} - \frac{2\cos t}{t^3}\right) ]

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The derivative of ( f(t) = (t - \sin(t), \frac{\cos(t)}{t^2}) ) with respect to ( t ) is:

[ f'(t) = \left(1 - \cos(t), \frac{-2\cos(t)}{t^3} - \frac{2\sin(t)}{t^3}\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) = (-1/(t+1) , e^(2t-1) ) #?
- How do you differentiate the following parametric equation: # x(t)=-2te^t+4t, y(t)= -2t^2-3e^(t) #?
- What is the derivative of #f(t) = (e^t/t +e^t, e^t-tcost ) #?
- How do you find #(d^2y)/(dx^2)# for the curve #x=4+t^2#, #y=t^2+t^3# ?
- How do you find the arc length of a parametric curve?

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