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New York Times
The Great Divide
Another Link in the Chain
Vague Instructions
100
This function allows us to find the slope of the tangent line at a given point.
What is the DERIVATIVE?
100
This is the derivative of f(x)= (x^2 +1)(x^2 -2x).
What is 4x^3 -6x^2 +2x -2?
100
This is the derivative of f(x)= x/(x^2 +1).
What is (1-x^2)/(x^2 +1)^2
100
This is the derivative of g(x)= 3(4-9x)^4.
What is -108(4-9x)^3?
100
This is dy/dx of x^2 -y^2=16.
What is x/y?
200
This is the formal definition of a derivative
What is the limit of f of x plus delta x minus f of x all over delta x as delta x approaches zero.
200
This is the derivative of h(t)= t^(1/3) (t^2 + 4)
What is (7t^2 +4)/(3t^(2/3))?
200
This is the derivative of g(t)= (t^2 +2)/(2t -7)
What is (2t^2 -14t -4)/(2t -7)^2?
200
This is the derivative of y= (9x^2 +4)^(1/3).
What is 6x/(9x^2 +4)^(2/3)?
200
This is dy/dx of (x^2)y+(y^2)x = -2.
What is (-y(y +2x))/(x(x+2y))?
300
This process allows us to find the derivative of a relationship that is not explicitly defined.
What is IMPLICIT DIFFERENTIATION?
300
This is the derivative of f(x)= x^3 cosx
What is 3x^2 cosx - x^3 sinx
300
This is the derivative of h(s)= s/(s^(1/2) -1).
What is (s^(1/2) -2)/2(s^(1/2) -1)^2?
300
This is the derivative of g(x)= 3tan4x.
What is 12(sec4x)^2?
300
This is dy/dx of (sin(pi)x + cos(pi)y)^2 = 2
What is (cos(pi)x)/(sin(pi)y)?
400
The derivative of a position function tells us this about an object.
What is the VELOCITY?
400
This is the derivative of g(x)= x^(1/2) sinx
What is x^(1/2) cosx + 1/(2x^1/2)) sinx?
400
This is the derivative of f(t)= (cos t)/(t^3).
What is -(t sint +3cost)/(t^4)?
400
This is the derivative of y= cos((1-2x)^2).
What is 4(1-2x)sin((1-2x)^2)?
400
This is dy/dx of y = sin(xy).
What is (ycos(xy))/(1 - xcos(xy))?
500
This is what we call variables that might all be changing together with respect to time.
What are RELATED RATES?