Find the second derivative of the polynomial. f(x) = -15x^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) = -15x^2. Using the power rule, which states that d/dx[x^n] = nx^(n-1), we apply it here: d/dx[-15x^2] = -15 * 2x^(2-1) = -30x. Find Second Derivative: Next, we find the second derivative of the polynomial. We take the derivative of the first derivative, -30x: d/dx[-30x] = -30 * 1x^(1-1) = -30.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the second derivative of the polynomial. $\newline$ $f(x) = -15x^2$ $\newline$ Write your answer as a polynomial in $x$ or as a constant. Simplify any fractions. $\newline$ $f''(x) =$ ______

View step-by-step help

Home

Math Problems

Calculus

Find higher derivatives of polynomials

Full solution

Q. Find the second derivative of the polynomial.

\newline

f(x) = -15x^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 $f(x) = -15x^2$ . Using the power rule, which states that $\frac{d}{dx}[x^n] = nx^{n-1}$ , we apply it here: $\newline$ $\frac{d}{dx}[-15x^2] = -15 \times 2x^{2-1} = -30x$ .
Find Second Derivative: Next, we find the second derivative of the polynomial. We take the derivative of the first derivative, $-30x$ : $\newline$ $\frac{d}{dx}[-30x] = -30 \times 1x^{(1-1)} = -30$ .