Calculus
Intermediate

Second Derivative

The derivative of the first derivative; measures concavity.

Formula

f′′(x)=ddx(f′(x))f''(x) = \frac{d}{dx}\left(f'(x)\right)

Variables

fFunction

Example

For s = t³, velocity s′ = 3t² and acceleration s″ = 6t.

Did You Know?

The second derivative measures acceleration — and tells you whether a curve is concave up or down.

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