Calculus Derivative Rules for Powers & +/-Constants. Fun Math Help Teaching Games by SliderMath Arithmetic Literacy.

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, where c and n can be positive or negative.

1) In general, the derivative power rule for y=xⁿ yields the derivative dy/dx = nx^n-1.
    For example, the derivatives of y=x⁴ and s(t)=t^-6 are respectively dy/dx=4x³ and s'(t)=-6t^-7.

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 = cnx^n-1.
    For example, the derivatives of y=-8x^-4 and g(t)=-3t⁶ are respectively y'=32x^-5 and g'(t)=-18t⁵.

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