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math: add higher order derivatives

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eggy 2020-10-28 17:18:50 -04:00
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@ -501,6 +501,15 @@ $$f´(x) = g´(h(x)) · h´(x)$$
$$f(x) = (4x^2-3x+1)^7$$ $$f(x) = (4x^2-3x+1)^7$$
$$f´(x) = 7(4x^2-3x+1)^6 (8x-3)$$ $$f´(x) = 7(4x^2-3x+1)^6 (8x-3)$$
### Higher order derivatives
The **second derivative** of $f(x)$ is the derivative of the first derivative of $f(x)$, that is, $f´´(x)$.
The $n$th derivative of $f(x)$ is $f^{(n)}(x)$, and is the derivative of the $n-1$th derivative. It is written as $\frac{d^ny}{dx^n}$ in Leibniz notation.
!!! example
The second derivative of an object's position with respect to time is its acceleration. See [SL Physics A#Displaying motion](/sph3u7/#displaying-motion) for more information.
## Resources ## Resources
- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf) - [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)