Answer :
Final Answer:
The answer of the given derivative that " f(x) = x⁷ - 3x⁵ + 8x³ - 4x - 9. Then f'(x) " os A) [tex]\(7x^6 - 15x^4 + 24x^2 - 4\)[/tex]
Explanation:
To find the derivative [tex]\(f'(x)\)[/tex] of the given function [tex]\(f(x) = x^7 - 3x^5 + 8x^3 - 4x - 9\),[/tex] we apply the power rule, which states that the derivative of [tex]\(x^n\)[/tex] with respect to x is [tex]\(nx^{n-1}\)[/tex].
So, taking the derivative term by term:
- The derivative of [tex]\(x^7\) is \(7x^6\)[/tex]
- The derivative of [tex]\(-3x^5\)[/tex] is [tex]\(-15x^4\)[/tex]
- The derivative of [tex]\(8x^3\) is \(24x^2\)[/tex]
- The derivative of [tex]\(-4x\) is \(-4\)[/tex]
- The derivative of the constant [tex]\(-9\) is \(0\)[/tex]
Putting all these derivatives together, we get [tex]\(f'(x) = 7x^6 - 15x^4 + 24x^2 - 4\).[/tex]
Therefore, the correct answer is A) [tex]\(7x^6 - 15x^4 + 24x^2 - 4\).[/tex]
