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=(x3x5)  is    y'=(x3)(5x4)+(3x2)(x5). - 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=xn yields the derivative  dy/dx = nxn-1.      For example, the derivatives of y=x4 and s(t)=t6 are respectively  dy/dx=4x3 and s'(t)=6t5.    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=8x4 and g(t)=5sin(t) are respectively y'=32x3 and g'(t)=5cos(t). - Three more examples of the Product Rule y'=uv'+u'v follow:    The derivative of y=(x3sin(x))  is    y'=(x3)(cos(x))+(3x2)(sin(x)).    The unsimplified derivative of y=2x3[8cos(x)]  is    y'=2x3[-8sin(x)]+6x2[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   Copyright © All Rights Reserved.
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