Calculus Derivative Rules for Powers & Constants Math Help Fun Game Tips:
- A derivative in Calculus can be described as an instantaneous rate of change.
The slope of a curve at a point P is an example of a derivative.
The speed of a moving particle at a time T is an example of a derivative.
- A sample curve or motion can be represented by a relation such as y=x2 or the equivalent f(x)=x2.
The derivative corresponding to y=x2 can be represented as dy/dx = 2x or y' = 2x or f'(x) = 2x.
The three derivative symbols dy/dx, y' and f'(x) are in common use by various authors.
- Similarly, the relation represented as s=t3 or s(t)=t3
has it's corresponding derivative represented as ds/dt = 3t2 or s'(t) = 3t2.
- A derivative power rule is used to get dy/dx = 2x from the given relation y=x2.
The same derivative power rule is used to get ds/dt = 3t2 from the given relation s(t)=t3.
- The following 3 derivative rules are used in this game, with n representing a positive integer.
1) In general, the derivative power rule for y=xn yields the derivative dy/dx = nxn-1.
For example, the derivatives of y=x4 and s(t)=t6 are respectively dy/dx=4x3 and s'(t)=6t5.
2) In general, the derivative constant rule for y=c yields the derivative dy/dx = 0.
For example, the derivatives of y=3 and s(t)=8 are respectively dy/dx=0 and s'(t)=0.
3) The derivative rule for a constant times a power such as y=cxn yields the derivative dy/dx = cnxn-1.
For example, the derivatives of y=8x4 and g(t)=3t6 are respectively y'=32x3 and g'(t)=18t5.
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