This is the second derivative of
f(x)=8x4-3x2-9x+18.
What is f''(x)=96x2-6?
100
A ball is thrown upward with an initial velocity of 60 m/s. After time t seconds, its height above the ground is given as
s(t)=5+60t-16t2. Find the velocity of the ball at 2 seconds.
What is -4 m/s?
100
For f(x)=√x, this is the derivative.
What is f'(x)=1
/2
√x?
100
The derivative of g(x)=1⁄x - 1⁄x2 is...
What is g'(x)=-1⁄x2 + 2⁄x3?
200
This is the rule necessary to take the derivative of y=3x-5⁄2x+1.
What is the quotient rule?
200
If y=e4x, dy/dx is equal to this.
What is dy/dx=4e4x?
200
This is the limit definition of the derivative.
What is f'(x)=limh →0f(x+h) - f(x)/h?
200
If y=83x, this is y'.
What is y'=3ln8(83x)?
200
For y=xe5x, this is the derivative.
What is y'=e5x(5x + 1)?
300
This is the derivative of y=ln(3x).
What is y'=1⁄x?
300
This is the derivative of
f(x)=x2 + 3x + 5/2x
What is f'(x)=x2 - 5/2x2?
300
This is the derivative of
g(w)=∛(w5 - 4w + 8).
What is g'(w)=(5w4 - 4)/3 ∛(w5 - 4w + 82)?
300
This is equation of the line tangent to the graph of f(x)=3x2 - 7x + 10 at x=-1.
What is y=-13x + 7?
300
For f(x)=(7x3 - 8x2 + 4x - 1)9, this is f'(x).
What is f'(x)=9(21x2 - 16x + 4)(7x3 - 8x2 + 4x - 1)8?
400
For g(x)=1⁄x, g'(x) is...
What is g'(x)=-1⁄x2
400
For y2 + 3xy - x3=7, this is dy/dx.
What is dy/dx=3x2 - 3y/2y + 3x?
400
The population of a culture of cells after t days is approximated by the function P(t)=1600/(1 + 7e-0.02t) for t ≥ 0. Determine the rate of change after 26 days.
What is about 5 cells per day?
400
This is the derivative of y=xx.
What is y'=xx(lnx + 1)?
400
This is the derivative of
f(x)=sinx/(cosx - 3) .
What is f'(x)=-3cosx + 1 /(cosx - 3)2?
500
The derivative is the slope of this line at any point.
What is the tangent line?
500
For g(x)=csc4(5x2 - x + 8), this is g'(x).
What is g'(x)=-4(10x-1)csc4(5x2 - x + 8)cot(5x2 - x + 8)?
500
Find the points on the graph of y=2x3/3 - 7x2/2 - 15x + 4 such that a tangent line is horizontal.
What are (-3⁄2 , 131⁄8) and (5 , -451⁄6)?
500
The second derivative of
g(x)=ln(x3 - 2x + 5) is this.
What is
g''(x)=-3x4 + 30x - 4/(x3 - 2x + 5)2?
500
Find an equation of the line tangent to the curve x2 + xy - y3 = 7
at (3, 2).