Final answer:
To find the derivative of the polynomial function f(x) = 6x^6 at the number a = 5, we use the power rule for differentiation.
Step-by-step explanation:
To find the derivative of the polynomial function f(x) = 6x^6 at the number a = 5, we can use the power rule for differentiation. The power rule states that if we have a term of the form ax^n, the derivative is given by nax^(n-1). Applying the power rule to the given function, we have f'(x) = 6 * 6x^(6-1) = 36x^5. To find f'(a) at a = 5, we substitute 5 for x in the derivative equation: f'(5) = 36 * 5^5 = 36 * 3125 = 112,500.