
Derivative Product Rule Practice with Sine Cosine & Power Rules Math Help Fun Game Tips:  The derivative Product Rule is used on the product of two relations such as the product y=uv. In general, the Product Rule states that the derivative of the product function y=uv is y'=uv'+u'v.  For example, the unsimplified derivative of y=(x^{3}x^{5}) is y'=(x^{3})(5x^{4})+(3x^{2})(x^{5}).  This game uses the Product Rule dy/dx = (u)(dv/dx) + (du/dx)(v) and also requires 4 other basic derivative rules: the Power Rule, the Sine Rule, the Cosine Rule, and the Constant times a Function Rule. Note that the symbols dy/dx, y' and f'(x) all represent the same derivative of y=f(x). 1) The derivative 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^{6} are respectively dy/dx=4x^{3} and s'(t)=6t^{5}. 2) The derivative Sine Rule for y=sin(x) yields the derivative dy/dx = cos(x). This means that the derivative of y=sin(x) is y'=cos(x). 3) The derivative Cosine Rule for y=cos(x) yields the derivative dy/dx =sin(x). This means that the derivative of y=cos(x) is y'=sin(x). 4) The derivative rule for a Constant times a Function such as y=cu yields the derivative dy/dx = c(du/dx). For example, the derivatives of y=8x^{4} and g(t)=5sin(t) are respectively y'=32x^{3} and g'(t)=5cos(t).  Three more examples of the Product Rule y'=uv'+u'v follow: The derivative of y=(x^{3}sin(x)) is y'=(x^{3})(cos(x))+(3x^{2})(sin(x)). The unsimplified derivative of y=2x^{3}[8cos(x)] is y'=2x^{3}[8sin(x)]+6x^{2}[8cos(x)]. The derivative of y=(2sin(x))(8cos(x)) is y'= 16sin(x)sin(x)+16cos(x)cos(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 snowflake hits.  The Game score is reduced by the number of snowflake 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 