
Derivative Chain Rule for Composite Functions Math Help Fun Game Tips:  A composite function such as y = (x^{3}+x^{4})^{20} represents a function of a function. In this case, y is a function of g. This means y = f(g) = g^{20} where g itself is a function of x , g = x^{3}+x^{4}.  The derivative Chain Rule states that the derivative of y = f(g) is dy/dx = (dy/dg)(dg/dx), which says the derivative of y with respect to x=(derivative of y with respect to g)times(derivative of g with respect to x). Consequently y= (x^{3}+x^{4})^{20} has the derivative dy/dx= (20g^{19})(3x^{2}+4x^{3}) which equals (20(x^{3}+x^{4})^{19})(3x^{2}+4x^{3})  Example 2: the unsimplified derivative of y= (x^{5}2x)^{7} is dy/dx = (7(x^{5}2x)^{8})(5x^{4}2)  Note: This game also uses the derivative Power rule for y=x^{n} which gives the derivative dy/dx = nx^{n1}.  The score report automatically appears after you have made 10 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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