# The position of an object moving along a line is given by #p(t) = t - tsin(( pi )/4t) #. What is the speed of the object at #t = 7 #?

According to the difference rule, we can write:

Use the chain rule:

Now we have:

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Calculate the derivative of the position function with respect to time and evaluate it at t = 7 to find the speed of the object. The speed is the magnitude of the derivative.

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