Show:
Definition of Derivatives
Derivative as a function
Product/ Quotient rule
Rates of change
Higher Derivatives
100
Use the definition of derivatives to compute the derivative for : F(X) = X^2 show all work
2X
100
Find Values of X for which the tangent line has a slope of 27 on f (x) = x^3 + 1
+3 and -3
100
F(X) = 2cosx / (1-sinx)^2
F'(x) = 2cosx / (1-sinx)^2
100
what is the rate of change of the function F(X) = X^3 + 10x^2 + 2x at x=2 ?
54
100
Find Y" if Y= 50x^5 + (3/x) - 7x^(-5/3)
Y"= 1000x^3 + (6/X^3) - (280x^(-11/3)/9)
200
Use the definition of derivatives to compute the derivative for : f(x)= (1/2)X - (3/5) Show all work
(1/2)
200
Find the function whose tangent line has the slope 3x^2 + 1 for each value of x and whose graph passes through (0, 2). A) x^3 + x + 2 B) x^3 + x C) x^3 + x −2 D) x^3+3
A
200
F(X)= 4x^3 - 3x^2 ---------------- 5x^7 + 1
F'(X) = -80x^9 + 75x^8 + 12x^2 - 6x
200
What is the instantaneous rate of change of the stopping distance of a car if the function of the stopping distance (in feet) is f (X) = .5x^2 + 1.3x + 2.5 and x=25
26.3 ft/mph
200
Find Y''' if y= 9x^4 + 6x^2 - 7x + 11
y"'= 216X
300
Use the definition of derivatives to compute the derivative for : F(X) = 5x^2 - 3x + 7 Show all work
10x - 3
300
Use the power rule to compute F(X) = x^10 at x=2
5120
300
(x^2 - 4x + 3)( x + 1 )
3x^2 - 6x - 1
300
If the velocity of a plane is v(t)= t^2 + 2t + 1 (in ft/s) what is the position of the plane at t= 5 seconds
(215/3) or 71.667 ft
300
Find y""' if Y= -xsinx + cosx
Y'''''= -xsinx + 5cosx
400
Use the definition of derivatives to compute the derivative for : F(X) = 4 - sqrt(x+3) Show all work
-1 / (2sqrt(x+3))
400
Calculate the derivative F(X) = x^6 + 3x^5 - 7x^4 + 2x^3 + x^2 + 17x - 300
F'(X)= 6x^5 + 15x^4 - 28x^3 + 6x^2 + 2x + 17
400
F(X) = 4x^8 - sqrt(X) ------------------ 8x^4
F'(X) = 32x^11 + 7x^(7/2) / ( 16x^8 )
400
s(t)= 2t^3 is the position of a race car along a straight track measured in feet from the starting line at time t seconds. What is the instantaneous rate of change of the race car at time t=4
96 ft/sec
400
Find Y''' if Y= 8x^10
Y'''= 720x^8
500
Use the definition of derivatives to compute the derivative for : F(X) = (x + 1)/(2 - x) Show all work
3 / (2 - x)^2
500
Calculate the derivative at X=12 F(X) = x^5 - 12x^3 +2x^2
98544
500
F(X) = ( x^4 - x^2 )( 2x^3 + x )
F'(X) = 6x^8 + 8x^6 - 5x^4 - 3x^2
500
Find the rate of change of the velocity function v(t)= 3x^2 + (2x/3) + 1 ( in ft/min) at time t=4.5 minutes
(83/3) or 27.667 ft/min^2
500
Find y''' if Y = ( 9x^3 + 15x^2 )( X^5 + 1 )
3024x^5 + 3150x^4 + 54