
Derivative Sum Rule Practice with Powers Math Help Fun Game Tips:  The derivative Sum Rule is used on a sum of terms such as y = u + v. In general, the Sum Rule states that the derivative of the sum function y = u + v is y' = u' + v'. This rule also includes the derivative of the function y = u  v , namely y' = u'  v'.  For example, the derivative of y = (x^{3} + x^{5}) is y' = (3x^{2}) + (5x^{4}).  The derivative of y = (2x^{3} + x^{5}) is y' = 6x^{2}  5x^{6}.  This game also uses the following two rules: 1) The Power Rule for y=x^{n} yields the derivative dy/dx = nx^{n1}. For example, the derivatives of y=x^{4} and s(t)=t^{4} are respectively dy/dx=4x^{3} and s'(t)=4t^{5}. 2) The derivative rule for a Constant times a Function such as y=cu yields the derivative dy/dx = c(du/dx). For example, the derivative of y=8x^{4} is y'=32x^{3}.  Note that the three symbols dy/dx, y' and f'(x) all represent the same derivative of y=f(x).  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. 
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