Derivative Practice

(Quotient Rule)

100

Find the derivative of: y = 

(-3(3x - 2x^2))/(7x)

What is: y'= 

6/7

200

Find the derivative of : y= 

What is : y'=

(-5x^2 + 4x +5)/(x^2 +1)^2

300

Find the derivative of: y= 

(1 - cos x)/ sinx

What is: y'= csc²x - cscx cotx.   or

(1- cosx)/ sin^2 x

400

Find the derivative of:  y= 

(x^2)/(2sqrtx + 1

What is: y' = 

(x(3sqrtx + 2))/(2sqrtx + 1)

500

Find the slope of the tangent line at (4,7) to:

 f(x)= 

What is: 

-17/4

600

Find an equation of the tangent line at (-1,1) of the graph: f(x) = [3 - (1/x)]/ (x +5)

What is:  y= 1 ?

(Chain Rule)

100

y=sin(cosx)

-cos(cosx)sinx

200

f(t)=sqrt(1-t)

f'(t)=-1/(2(1-t)^1/2)

300

s(t)=1/(t^2+3t-1)

(-2t-3)/(t^2+3t-1)^2

400

y=(2x-7)^3

y'=6(2x-7)^2

500

y=sin(pi x)

y'=pi cos(pi x)

600

y=x²e^x-2xe^x+2e^x

y'=x²e^x

(Product Rule)

100

Find the derivative of:  y=(3x-2x²)(5 + 4x)

What is:  y' = -24x² +4x + 15.

200

Find the derivative of:  y= 3x²sin(4x).

What is: y'= 6x[sin(4x) + 2xcos(4x)]

300

Find the derivative of: y= sin x cos x

What is:  y'= cos²x - sin²x

400

Find the derivative of:  y = (x² +3)(5x⁴ -(1/x))

What is: y'=  30x⁵ + 60x³ + (3/x²) - 1

500

Find the derivative of:  f(x)= y=sin(tan 2x)

What is :  2cos(tan 2x)(sec²(2x))

or

[2cos(tan 2x)]/(cos²(2x))

600

Find y'(2), if : y = (x - 4)(x² + 6x -1)

What is: -5

ANYTHING

100

Find the derivative of f(x) = [ cos(2x) ]²

What is: -4[cos(2x)](sin(2x))

200

Find the derivative of f(x) = sin²(4x)

What is 8 sin (x) cos (x)?

300

Find the slope of f(x)= (5/x³) - 3(x²)- (1/x) at x = -1

What is -8?

400

The slope of the normal line to the curve y= (2x²) + 1 at (1,3) is

What is -1/4 ?

500

 A car is moving along a straight road. The position of the carat a time is given by the function s(t). The velocity of the car is the derivate of the position of the car, v(t) = s'(t). If the position function is s(t) = 3t² + 2t+ 5, determine the velocity at t=2

14 units

600

A rocket is launched vertically from the ground. The height of the rocket above the ground at time t is modeled by the function ℎ(t)=−5t²+2t+5 where is measured in meters and t is measured in seconds. What is the maximum height?

9/5

Roe Trivia

100

Mr. Roe's favorite snack 

What are Fig Newtons?

200

Mr Isaac Roe graduated from what UNiversity

What is Arizona State?

300

Mr. Ethan Roe graduated from what College?

What is Wabash College?

400

Mr. Roe got his master's degree at what college?

What is Providence College?

500

How many sheep are on the Roe farm?

What is 2?

600

The year Mr. Roe started working at BMR

What is 1996?