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

Find First Derivative: First, we need to find the first derivative of the polynomial f(x) = 2x^2. Using the power rule, which states that d/dx[x^n] = nx^(n-1), we apply it here: d/dx[2x^2] = 2 * 2x^(2-1) = 4x. Find Second Derivative: Next, we find the second derivative of the polynomial by differentiating 4x. Again, using the power rule: d/dx[4x] = 4 * x^(1-1) = 4 * x^0 = 4.

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

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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) = 2x^2

\newline

Write your answer as a polynomial in

x

or as a constant. Simplify any fractions.

\newline

f''(x) =

______

Find First Derivative: First, we need to find the first derivative of the polynomial $f(x) = 2x^2$ . Using the power rule, which states that $\frac{d}{dx}[x^n] = nx^{(n-1)}$ , we apply it here: $\newline$ $\frac{d}{dx}[2x^2] = 2 \times 2x^{(2-1)} = 4x$ .
Find Second Derivative: Next, we find the second derivative of the polynomial by differentiating $4x$ . Again, using the power rule: $\newline$ $d/dx[4x] = 4 \times x^{1-1} = 4 \times x^0 = 4$ .