Second derivative of a polynomial

Let $f(x) = x^5 - 4x^3 + 2x$ .

Find $f''(x)$ .

Hint

First find $f'(x)$ using the power rule term by term, then differentiate again.

Step-by-step solution

Differentiate $f(x) = x^5 - 4x^3 + 2x$ term by term using the power rule: $f'(x) = 5x^4 - 12x^2 + 2$ .

Differentiate $f'(x)$ again term by term: $f''(x) = 20x^3 - 24x$ .

Third derivative of a polynomial

Find $f'''(x)$ .

Hint

Differentiate the second derivative $f''(x) = 20x^3 - 24x$ one more time using the power rule.

Step-by-step solution

Starting from $f''(x) = 20x^3 - 24x$ , apply the power rule term by term one more time.

This gives $f'''(x) = 60x^2 - 24$ .

Hint

Step-by-step solution

In $f'''(x) = 60x^2 - 24$ , the constant term (the number standing alone without any $x$ ) is $-24$ .