High School

Find the derivative of the function [tex]f(x) = -\frac{5}{2}x^9[/tex].

A) [tex]-45x^8[/tex]

B) [tex]-45x^9[/tex]

C) [tex]-5x^8[/tex]

D) [tex]-5x^9[/tex]

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.