Second derivative

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In physics and mathematics, the second derivative is the derivative of the derivative of a function, say f(x). The second derivative has many real-life applications, especially in the study of acceleration. Second derivatives can be notated in several ways, some of which are

\frac{d^2x}{dy^2} or f''(x)

Other notations are used, but the above two are the most commonly used.

Power Rule for Finding the Second Derivative[change | edit source]

If we have a function f(x)=x^n, then the second derivative of the function can be found using the power rule for second derivatives

\frac{d^2x}{dy^2}[x^n]=(n^2-n)x^{n-2}=n(n-1)x^{n-2}