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secondderivative

second derivative

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There are 16 letters in SECONDDERIVATIVE ( A¹C³D²E¹I¹N¹O¹R¹S¹T¹V⁴ )

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Definitions of second derivative in various dictionaries:

SECOND DERIVATIVE - In calculus, the double derivative, or the double anti-integral, of a function f is the derivative of the derivative of f. Roughly speaking, the sec...

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Second derivative description
In calculus, the double derivative, or the double anti-integral, of a function f is the derivative of the derivative of f. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of a vehicle with respect to time is the instantaneous acceleration of the vehicle, or the rate at which the velocity of the vehicle is changing with respect to time. In Leibniz notation:* * * * * a * * = * * * * d * * v * * * * d * t * * * * = * * * * * d * * 2 * * * * x * * * * d * * t * * 2 * * * * * * , * * * {\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}{\boldsymbol {x}}}{dt^{2}}},} * where the last term is the second derivative expression. * On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the opposite way.

Second derivative description

In calculus, the double derivative, or the double anti-integral, of a function f is the derivative of the derivative of f. Roughly speaking, the second derivative measures how the rate of change of a quantity is itself changing; for example, the second derivative of the position of a vehicle with respect to time is the instantaneous acceleration of the vehicle, or the rate at which the velocity of the vehicle is changing with respect to time. In Leibniz notation:*
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* {\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}{\boldsymbol {x}}}{dt^{2}}},}
* where the last term is the second derivative expression.
* On the graph of a function, the second derivative corresponds to the curvature or concavity of the graph. The graph of a function with a positive second derivative is upwardly concave, while the graph of a function with a negative second derivative curves in the opposite way.

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