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higher-order derivative

The derivative of a derivative — how the rate of change is itself changing.

The second derivative f''(x) is the derivative of f'(x); continuing gives the third derivative f'''(x), and so on. f'' measures concavity; for position functions, f'' is acceleration.

Examples

  • For f(x)=x^4: f''(x)=4x^3, f''''(x)=12x^2, f''''''(x)=24x.

See also

derivative concavity
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