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Step 1---
**Solution:** *Step 1: Recall the product rule for derivatives.* *Step 4: Apply the product rule.* Using the product rule, we get: \begin{align*} f'(x) &= g'(x)h(x) + g(x)h'(x) \ &= (15x^2)(cos(x)) + (5x^3)(-sin(x)) \end{align*} *Step 5: Simplify the expression.* \begin{align*} f'(x) &= x^2(15cos(x) - 5xsin(x)) \end{align*} **
Final Answer
** The derivative of the function f(x) = 5x^3 cos(x) is f'(x) = x^2(15cos(x) - 5xsin(x)).
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