Answer :
Final answer:
The derivative of the function f(x) = [tex]6x^8 + 2x^4 - 15x^2 + 9[/tex] is found by applying the power rule of differentiation, resulting in f'(x) = [tex]48x^7 + 8x^3 - 30x[/tex], which matches option A.
Explanation:
To find the derivative of the function f(x) = [tex]6x^8 + 2x^4 - 15x^2 + 9[/tex], we apply the power rule of differentiation. To use this rule effectively, recall that the derivative of a term [tex]ax^n[/tex] is given by [tex]nax^(n-1)[/tex]. Applying this to each term in the given function:
- The derivative of [tex]6x^8 is 48x^7[/tex].
- The derivative of [tex]2x^4 is 8x^3[/tex].
- The derivative of [tex]-15x^2[/tex] is -30x.
- The derivative of the constant 9 is 0, since the derivative of any constant is zero.
Combining these results yields the derivative f'(x) = [tex]48x^7 + 8x^3 - 30x[/tex]. Therefore, the correct option representing the derivative of the function is A) [tex]48x^7 + 8x^3 - 30x[/tex].
