Basic Derivatives
Complex Derivatives
Integration
Theorems
Word Problems
100
The derivative of 7x3+9x2+5x?
What is 21x2+18x+5.
100
What is the derivative of y=tan(3x2)
What is 6xsec2(3x2)?
100
∫x2dx=?
What is x3/3 +c?
100
According to the Fundamental Theorem of Calculus, ∫ab f(x)dx= ?
Hint: F(x) is the antiderivative of f(x)
What is F(b)-F(a)?
100
The area of the region bounded by f(x)=x2-3x-10 and g(x)=-x2+5x+14.
Note: Calculator Allowed, answer to three decimals.
What is 170.667?
200
The derivative of f(x)=3/2x2
What is -3x?
200
Derivative of:
ln(x3+3x2+7)
What is (3x2+6x)/(x3+3x2+7)?
200
Find the equation of F given F '(x)=
x3-3x2+7x+8 and F(0)=5.
What is F(x)=x4/4-x3+(7/2)x2+8x+5?
200
Using the second Fundamental Theorem of Calculus find F'(x) when F(x)=∫2x(9t+9)dt.
What is F’(x)=9x+9?
200
Find the average acceleration of a particle over the interval (0,50) given v(50)=80 ft/sec and the initial velocity of 10 ft/sec. Include units.
What is 7/5 ft/sec2?
300
The slope of f(x) at x= -1.
f(x) = 5/3x3-3x2-1/x2
What is 9?
300
dy/dx of:
xy2+y3+x2=10
What is (-2x-y2)/(2xy+3y2)?
300
Integrate:
∫2xcos(x2)sin2(x2) dx
What is (1/3)(sin x2)3+c
300
Using the second Fundamental Theorem of Calculus find F'(x) when F(x)=∫-32x(t+7t3)dt. Simplify.
What is 4x+112x3?
300
The rate of change of the radius r of a circle is 4cm/sec. Find the rate of change of Area A when r=2cm.
What is 16π ?
400
Find the derivative of f(x)=(x+3)3/(x-2)2-7x3-7x2.
Please DO NOT simplify.
What is {[(x-2)2-7x3-7x2]*[3(x+3)2]} - {[(x+3)3][2(x-2)-21x2-14x]} / [(x-2)2-7x3-7x2)2 .
400
dy/dx for the following function:
x2y3+y2+3x=y
What is (-3-2xy3)/(3x2y2+2y-1)?
400
∫(x)/(4+x2)1/2dx
What is (4+x2)1/2+c?
400
Given that f(x) is differentiable on [-2,2], find the value of f'(c) that satisfies the Mean Value Theorem on [-2,2] for f(x)=2x3+6x-2
What is 14?
400
The acceleration of a particle is given by the function a(t)=3t2+7. Find the position function of the particle given that its initial velocity is 10m/sec and its initial height is 80m.
What is t4/4 +3.5t2 +10t +80?
500
Find the derivative of f(x)=x2-5x+3 using the limit process.***Note: You Must Show Work!!!
What is 2x-5?
500
Find dy/dx at the point (12,17) for the function:
y2=3x2+4x+y
What is 76/33?
500
Solve for y=f(x) when dy/dx=x2+3x/y2 and f(3)=2.
What is y=[x3+(9/2)x2-(119/2)]1/3 ?
500
Find the value of c that satisfies the mean value theorem for the function y = sin(x)/x on the interval [-π,π].
What is Mean Value Theorem does not apply due to a discontinuity at x=0.
500
Find the volume of the solid generated by revolving the region bounded by y=x2, the x-axis, and x=2 around the y-axis.
What is 8π?