Second derivative facts for kids
In physics and mathematics, the second derivative is the derivative of the derivative of a function, say 
. 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
or 
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 
, 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}](/images/math/d/6/9/d695fe7199fdf4ce1f5f51bf80cd179b.png)
Images for kids
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A plot of f(x) = \sin(2x) from -\pi/4 to 5\pi/4. The tangent line is blue where the curve is concave up, green where the curve is concave down, and red at the inflection points (0, \pi/2, and \pi).
See also
In Spanish: Derivada de segundo orden para niños
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Second derivative Facts for Kids. Kiddle Encyclopedia.