Second derivative

In physics and mathematics (particularly in differential calculus), 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 mathematical optimization and acceleration. Second derivatives can be notated in several ways, some of which are

{\frac {\mathrm {d} ^{2}f}{\mathrm {d} x^{2}}}

,

{\frac {\mathrm {d} ^{2}y}{\mathrm {d} x^{2}}}

or

f''(x)

[1][2][3]

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

Power Rule for Finding the Second Derivative

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. That is,

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

Related pages

Second derivative test

References

"List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-09-16.
"Second Derivatives". Math24. Retrieved 2020-09-16.
"Content - The second derivative". amsi.org.au. Retrieved 2020-09-16.

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[1] "List of Calculus and Analysis Symbols". Math Vault. 2020-05-11. Retrieved 2020-09-16.

[2] "Second Derivatives". Math24. Retrieved 2020-09-16.

[3] "Content - The second derivative". amsi.org.au. Retrieved 2020-09-16.