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Answer :
Final answer:
To find the derivative of f(x)=-(5)/(2)x^(9), the power rule is applied, leading to the derivative being -45x^8, making the correct answer A) -45x^8.
Explanation:
To find the derivative of the function f(x) = -(5)/(2)x9, we apply the power rule of differentiation. The power rule states that the derivative of xn is nxn-1, where n is a constant.
In this case, our function is a polynomial function where the power of x is 9, and it is multiplied by the constant -(5)/2.
Applying the power rule, we multiply the exponent 9 by the constant factor -(5)/2 and decrease the exponent by 1. This yields:
Derivative: -((5)/2)*9*x8 = -45x8/2 = -45x8
Therefore, the correct answer is A) -45x8.
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