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

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the second derivative of the polynomial. $\newline$ $f(x) = -x^2$ $\newline$ 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) = -x^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 $f(x) = -x^2$ . Using the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ , we apply it here: $\newline$ $f'(x) = \frac{d}{dx}(-x^2) = -2x$
Find Second Derivative: Next, we find the second derivative by differentiating $f'(x) = -2x$ once more. Again, using the power rule: $\newline$ $f''(x) = \frac{d}{dx}(-2x) = -2$