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

There are two different derivatives depending on what you want to know about the function. One of them provides the velocity (a vector), and one provides the slope (a scalar).

Therefore, our velocity derivative is:

The slope of this function can be found with:

Final Answer

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The derivative of ( f(t) = \left(\frac{e^t}{t} + e^t, e^t - \cos(t)\right) ) is ( f'(t) = \left(\frac{e^t(t-1) + e^t}{t^2}, e^t + \sin(t)\right) ).

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