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 = nxn-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 = cnxn-1.     For example, the derivatives of y=-8x-4 and g(t)=-3t6 are respectively y'=32x-5 and g'(t)=-18t5. - The score report automatically appears after you have made 15 choices. - The Math score is based on your choices only and does not count the fish hits. - The Game score is reduced by the number of fish hits. - The game can be played using the mouse by itself or using the keyboard by itself. - If the game doesn't respond to keyboard input, click inside the game area to reset the game's focus. - Adjust the game's speed by pressing the + or - key repeatedly. - Refresh/Reload the webpage to start over again. More SliderMath   Copyright © All Rights Reserved.
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