find the derivative for f(x) = 5x^4 - 8x^2 + 8.6 answer 2 points f(x) =

Explanation:

Step1: Apply power - rule to first term

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$. For the term $5x^4$, $a = 5$ and $n = 4$. So the derivative of $5x^4$ is $5\times4x^{4 - 1}=20x^3$.

Step2: Apply power - rule to second term

For the term $-8x^2$, $a=-8$ and $n = 2$. So the derivative of $-8x^2$ is $-8\times2x^{2 - 1}=-16x$.

Step3: Apply rule for constant term

The derivative of a constant $C$ is 0. Since 8.6 is a constant, its derivative is 0.

Step4: Combine derivatives

$f^\prime(x)$ is the sum of the derivatives of each term. So $f^\prime(x)=20x^3-16x + 0$.

Answer:

$20x^3-16x$