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Related Rates
Product Rule
Power Rule
Chain Rule
Quotient Rule
100
What does a derivative tell us?
What is How fast something is changing
100
h'(x)= f'(x) * g(x) + g'(x) * f(x)
What is Product rule formula
100
f(x)= 3^3(x2^1/2)
What is 3x^2/3
100
y=(x^3+x-1)^5
What is 5(x^3+x-1)^4(3x^2+1)
100
f(x)=(x^2-2)/(x^2+1)
What is (6x)/(x^2+1)^2
200
Pumped in a rate of 4.5 inches^3 over a minute. How fast is the radius changing when r= 2 inches?
What is .0895inches/minute = dr/dt
200
f(x) = x^2(x^2+4)
What is f'(x) = -1x^3+8x
200
g(x)=1/x^4+1/x^3
What is g'(x)=-4x^-5-3x^-4
200
(x^2+1)^4
What is 8x(x^2+1)
200
(x^2-2)/(x^3+1)
What is (-x^4+6x^2+2x)/(x^3+1)^2
300
A template ladder leaning against a side of a building begins to fall down a wall at 2 feet per second, how fast is the bottom of the ladder sliding away from the wall when the top of the ladder is 8 feet off the ground.
What is 8/3 feet per second.
300
f(x)= (2x+3)(x^2-5)
What is f'(x)= 6x^2+6x-10
300
f(x)=1/5x^20+3x^-3
What is f'(x)= 4x^19-9x^-4
300
(-2x^2+1)^1/2
What is -2x(-2x^2+1)^-1/2
300
(x^3+5)/(2x+1)
What is (4x^3+3x^2-10)/(2x+1)^2
400
A car is traveling at 50 miles per hour due south, at a point 1/2 miles north of an intersection. A police car is traveling at 40 miles per hour due westat a point 1/4 miles east of the same intersection. At that instant the radar in the police car measures the rate at which the distance between the two car is changing, what does the radar gun register?
What is 62.6 miles per hour
400
f(x)= x^1/2 (x^1/2-3)
What is f'(x)= -3/2x^-1/2 +1
400
g(x)=-3x^50+1/5x^5
What is G'(x)= -150x^149+x^4
400
(x^2+1)^3
What is 3(x^2+1)^2(2x)
400
(x^1/2+3)/(x^1/2-1)
What is (-2x^-1/2)/(x^1/2-1)^2
500
A small company estimates that when it spends (x) thousand dollars for advertising in a year its annual sales will be be described by s= 60 - 40e^-.05(x) thousand dollars.The 4 most recent annual advertising totals are given in the following table. YEAR: 1 2 3 4 DOLLARS: 14500 16000 18000 20000
What is 1472 per year
500
f(x)= x^3*sinx
What is f'(x)= 3x^2sinx + x^3cosx
500
f(x)= 20x^3-1/2x^-5
What is f'(x)= 60x^2+5/2x^-6
500
((x^2+4)^(1/2)-3x^2)^3/2)
What is 2/3((x^(2)+4)^(1/2)-3x^2)^(1/2)(x(x^(2)+4)^(1/2)-6x)
500
What is the formula
What is h'(x)=(f'(x))(g(x))-(g'(x))(f(x))/g(x)^2