`f(t) = 2(t^5)cos(t)` Use the Product Rule or the Quotient Rule to find the derivative of the function.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to evaluate the derivative of the given function and since the function is a product of two polynomials, then you must use the product rule, such that:

`f'(t) = (2t^5)'(cos t) + (2t^5)(cos t)'`

`f'(t) = (10t^4)(cos t) + (2t^5)(-sin t)`

Hence, evaluating the derivative of the function, using the product rule, yields` f'(t) = (10t^4)(cos t) - (2t^5)(sin t).`