Find the second derivative of the polynomial. f(x) = 5x^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) = 5x^2. Using the power rule, which states that d/dx[x^n] = nx^(n-1), we apply it here: d/dx[5x^2] = 5 * 2x^(2-1) = 10x. Find Second Derivative: Next, we find the second derivative of the polynomial by differentiating 10x once more. Again, using the power rule: d/dx[10x] = 10 * 1x^(1-1) = 10.

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Find the second derivative of the polynomial. $\newline$ $f(x) = 5x^2$ $\newline$ Write your answer as a polynomial in $x$ or as a constant. Simplify any fractions. $\newline$ $x$ = $\_\_\_\_\_\_$

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Find higher derivatives of polynomials

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Q. Find the second derivative of the polynomial.

\newline

f(x) = 5x^2

\newline

Write your answer as a polynomial in

x

or as a constant. Simplify any fractions.

\newline

x

\_\_\_\_\_\_

Find First Derivative: First, we need to find the first derivative of the polynomial $f(x) = 5x^2$ . Using the power rule, which states that $\frac{d}{dx}[x^n] = nx^{n-1}$ , we apply it here: $\newline$ $\frac{d}{dx}[5x^2] = 5 \times 2x^{2-1} = 10x$ .
Find Second Derivative: Next, we find the second derivative of the polynomial by differentiating $10x$ once more. Again, using the power rule: $\newline$ $\frac{d}{dx}[10x] = 10 \times 1x^{1-1} = 10$ .