Derivative of a f(x)
Derivatives of trigonometric functions
Velocity and Rate of Change
Chain Rule
Derivatives of Exponential and Logarithmic Functions
100
f(x)=x^2
What is f'(x)=2x
100
f(x)=1 + x - cosx
What is f'(x)=1 + sinx
100
A particle moves along a line so that is position at any time is at or above T=0 is given by the function: s(T)=T^2-3T+2 (a) Find the displacement at T=5 (in meters) (b) Find the velocity at T=5 ( in m/s)
What is: (a) 12 m (b) 7 m/s
100
f(x)=(x+2)^2
What is f'(x)=2x+4
100
Find the derivative of f(x)=2e^x
What is f'(x)=2e^x
200
f(x)=3x^8
What is f'(x)=24x^7
200
f(x)=2sinx - cosx
What is f'(x)=2cosx + sinx
200
A particle moves along a line so that its position at any time is at or above T=0 is given by the function: s(T)=T^3-6T^2+8T+2. When is the particle at rest?
What is T= 2+[2(root 3)/3]
200
f(x)=3(x^2+4)^5
What is f'(x)=30x(x^2+4)^4
200
Find the derivative of f(x)=3e^-x
What is f'(x)=-3e^-x
300
f(x)=5/x^4
What is f'(x)=-20/x^5
300
f(x)=1/x + 5sinx
What is f'(x)=-1/x^2)+ 5cosx
300
The number of gallons of water in a tank T minutes after the tank has started to drain is q(T)=200(30-T)^2. How fast is the water running out at the end of 5 minutes? Make sure answer is in gal/min.
What is -1000 gal/min
300
f(x)=4x(7x^2+3x+4)^2
What is f'(x)=8x(7x^2+3x+4)*(14x+3)
300
Find the derivative of f(x)=xe^2-e^x
What is f'(x)=e^2-e^x
400
f(x)=5(root x^3)
What is f'(x)=15(root x) all over 2
400
f(x)=4 - x^2(sinx)
What is f'(x)=-x^2cosx - 2xsinx
400
The equations for free fall near the surfaces of Mars and Jupiter (s in meters, t in seconds) are: Mars, s=1.86t^2; Jupiter, s=11.44t^2. How long would it take a rock falling from rest to reach a velocity of 16.6 m/s (about 60km/h) on each planet?
What is: Mars --> about 4.46 seconds Jupiter --> about 0.726 seconds
400
f(x)=2x^2(14x+7)^3 - 18x^3
What is f'(x)=4x(14x+7)^3+84x^2(14x+7)^2-54x^2
400
Find the derivative of f(x)=ln(x^2)-ln(x)
What is f'(x)=1/x
500
f(x)=4/(root x^3) + 3/x^7
What is f'(x)=-6/(root x^5) - 21/x^8
500
f(x)=cotx/(1 + cotx)
What is f'(x)=-(csc^x/(1 + cotx)^2))
500
Although the November 1959 Kilauea Iki eruption on the island of Hawaii began with a line of fountains along the wall of the crater, activity was later confined to a single vent in the crater's floor, which at one point show lava 1900 ft straight into the air (a world record). What was the lava's exit velocity in feet per second? [Hint: If Vo is the exit velocity of a particle of lava, its height T seconds later will be s=VoT-16T^2 feet. Begin by finding the tame at which ds/dT=0. Neglect air resistance.]
What is approximately 348.712 ft/s
500
f(x)=3x(16x^4+17x)^3/(1/x + 15)^2
What is f(x)=[3(16x^4+17x)^3+576x^4+153x+2/x^2(1/x+15)] all over (1/x+15)^4
500
Find the derivative of f(x)=log(base 10)of e^x
What is f'(x)=1/ln(10)
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