math: rearrange rules to latest and tell people rules are good
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@ -436,8 +436,21 @@ results in the equation of the derivative function. Direct substitution of $h$ w
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f´(x)=4x
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$$
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### Drawing derivative functions
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If the slope of a tangent is:
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- positive/negative, that value on the derivative graph is also positive/negative, respectively
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- zero, that value on the derivative graph is on the x-axis
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Points of inflection on the original function become maximum/minimum points on the derivative graph.
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The derivative of a linear equation is always constant, and the derivative of a constant value is $0$..
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### Derivative rules
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These rules can be used in place of/to supplement finding derivative functions using first principles and are usually much faster to calculate.
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The degree of a derivative is always the degree of the original function$-1$.
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The **power rule** applies to all functions of the form $f(x)=x^n,x \in \mathbb{R}$, such that:
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@ -462,17 +475,6 @@ $$f´(x) = g´(x) + h´(x)$$
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$$f(x) = 2x^2 + 3x$$
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$$f´(x) = 4x + 3$$
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### Drawing derivative functions
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If the slope of a tangent is:
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- positive/negative, that value on the derivative graph is also positive/negative, respectively
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- zero, that value on the derivative graph is on the x-axis
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Points of inflection on the original function become maximum/minimum points on the derivative graph.
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The derivative of a linear equation is always constant, and the derivative of a constant value is $0$..
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## Resources
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- [IB Math Analysis and Approaches Syllabus](/resources/g11/ib-math-syllabus.pdf)
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