# What is the derivative of #f(t) = (t^3-e^(3t-1) , -t^2-e^t ) #?

Derivative is

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The derivative of (f(t) = (t^3 - e^{3t - 1}, -t^2 - e^t)) with respect to (t) is given by:

[\frac{d}{dt}f(t) = \left(\frac{d}{dt}(t^3 - e^{3t - 1}), \frac{d}{dt}(-t^2 - e^t)\right)]

Solving each component separately:

[\frac{d}{dt}(t^3 - e^{3t - 1}) = 3t^2 - 3e^{3t - 1}]

[\frac{d}{dt}(-t^2 - e^t) = -2t - e^t]

Therefore, the derivative of (f(t)) with respect to (t) is:

[\frac{d}{dt}f(t) = (3t^2 - 3e^{3t - 1}, -2t - e^t)]

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