Simple Dervatives
What is the derivative of 4x7
28x6
Find dy/dx by implicit differentiation for x/y3=1
y/3x
What is the equation of the tangent line to y=x2 at x=2
y=4x-4
Find the point of inflection for f(x) = x3-6x2+12x-5
x = 2
A particle moving right along the x axis has a velocity modeled by the function v(t)= lnx +e^x. Find the acceleration function
1/x+e^x
What is the derivative 3x4tan(x)?
3(4x3tan(x)+x4sec(x))
Find dy/dx by implicit differentiation for 7y2+sin(3x)=12−y4
dy/dx = -3cos(3x) / 14y+4y3
What is the equation of the tangent line to y = -4x3+7x2-9x+12 at (1,6)
y=-7x+13
Let f(x) = 5x3 + 2x2 - 3x. Find interval of concave down.
(-infinity, -2/15)
A particle particle is moving right along the x axis and has a velocity modeled by the function v(t)= x^2-4x+4 on the interval (0,4). When does the function decrease
(0,2)
What is the derivative of (3x-9/2-x)?
15/(2-x)2
Find dy/dx by implicit differentiation for exy=e4x-e5y
(4e4x-yexy) / (xexy+5e5y)
If y=16x-1-x2. At what point is the tangent line horizontal?
Find the point(s) of inflection: f(x) = -7x4+5x2-x+3
(You may need a calculator)
(-sqrt(5/42), sqrt(5/42) + 881/252), (sqrt(5/42), -sqrt(5/42)+ 881/252)
A particle is moving right along the x axis and has a position function modeled by the equation y = 3cos(3x). Find all points in the interval (0,pi) where the function changes from increasing to decreasing or decreasing to increasing
pi/3 and 2pi/3
What is the derivative of 5ex/3ex+1?
5ex/(3ex+1)2
Find d2y/dx2 by implicit differentiation for 2x2-3y2=4
2(3y2-x2)/9y3
What is the equation of the tangent line to y2e2x=3y+x2 at (0,3)
y=-6x+3
Let f(x) = x6/30 - x5/20 - x4 + 3x + 20. Find the intervals of concave up.
(-infinity, -3) U (4 , infinity)
A particle is moving right along the x axis and has the position function s(t)= 3cos(x) +e^x+ 3tan(x). Find the acceleration function
-3cos(x)+e^x+6sec^2(x)tan(x)
What is the derivative of 2x/cos5(5x)?
2x(ln(2)cos(5x)+20sin(5x)) / cos6(5x)
Find d2y/dx2 by implicit differentiation for xy + y2=2
2y(x+y) = (x+2y)3
A line normal (perpendicular) to the curve y=2x2 at a point in the first quadrant also passes through the point (0,3/4). Find an equation for this line
y=(-1/2)x+3/4
Find and identify the relative extrema for f(x) = 5x5 - 7x4 + 8x3 - x + 8
(-0.1827, 8.125) (relative max)
(0.2301, 7.851) (relative min)
A particle p is moving along the x axis. At time t=0, the particle's position s(t) is equal to 9. The velocity of the particle is given by the equation v(t)= 2x^2 +4. Write but do not solve an equation to find the position of the particle at t=5
s(0)+int(2x^2 +4) from 0 to 5