Find the second derivative of the polynomial. f(x) = -8x^2 Write your answer as a polynomial in x or as a constant. Simplify any fractions. (x) = ______

Find First Derivative: To find the second derivative, we first need to find the first derivative of the polynomial f(x) = -8x^2. Using the power rule, which states that d/dx[x^n] = n*x^(n-1), we apply it here: d/dx[-8x^2] = -8 * 2x^(2-1) = -16x. Find Second Derivative: Next, we find the second derivative by differentiating -16x once more. Applying the power rule again: d/dx[-16x] = -16 * 1x^(1-1) = -16.

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Find the second derivative of the polynomial. $\newline$ $f(x) = -8x^2$ $\newline$ Write your answer as a polynomial in $x$ or as a constant. Simplify any fractions. $\newline$ $x$ = ______

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Calculus

Find higher derivatives of polynomials

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Q. Find the second derivative of the polynomial.

\newline

f(x) = -8x^2

\newline

Write your answer as a polynomial in

x

or as a constant. Simplify any fractions.

\newline

x

= ______

Find First Derivative: To find the second derivative, we first need to find the first derivative of the polynomial $f(x) = -8x^2$ . Using the power rule, which states that $\frac{d}{dx}[x^n] = n\cdot x^{(n-1)}$ , we apply it here: $\newline$ $\frac{d}{dx}[-8x^2] = -8 \cdot 2x^{(2-1)} = -16x$ .
Find Second Derivative: Next, we find the second derivative by differentiating $-16x$ once more. Applying the power rule again: $\newline$ $\frac{d}{dx}[-16x] = -16 \times 1x^{(1-1)} = -16$ .