Chapter 2 Review: Derivatives

Question 1

For the graph below, does f'(0) exist?

Accepted Answer

no

Question 2

If f has a derivative at x=a, then f is continuous at x=a.

Accepted Answer

True

Question 3

Find dy/dx for y = (x) / (1 + cos(x))

Accepted Answer

[1+cos(x)+xsin(x)] / [1+2cos(x)+cos2(x)]

Question 4

Use the limit of the difference quotient to determine the derivative of f(x)=x3

Accepted Answer

3x2

Question 5

Using implicit differentiation, find dy/dx for x2 - xy + x2 = 7

Accepted Answer

dy/dx = (y-2x) / (2y-x)

Question 6

Find f'(x) for f(x) = (x2+1)(x3+3)

Accepted Answer

5x4+3x2+6x

Question 7

Find dr/dx for r = tan(2-x)

Accepted Answer

-sec2(2-x)

Question 8

Which of the following is not true about the derivatives of trig functions?

Accepted Answer

d/dx sin(x) = -cos(x)

Question 9

Find y' for y=sin-1(1-t)

Accepted Answer

-1 / sqrt(2t-t2)

Question 10

Which of the following is not true about the derivatives of trig functions?

Accepted Answer

d/dx csc(x) = csc(x)cot(x)

Question 11

Who is responsible for discovering Calculus?

Accepted Answer

Issac Newton and Gottfried Wilhelm von Leibniz

Question 12

The function y = (x)2/3 fails to be differentiable at x=0, what type of problem is at x=0?

Accepted Answer

cusp

Question 13

Find an equation for the line tangent to the curve f(x)= (x3+1) / (2x) at x=1

Accepted Answer

y - 1 = 1/2(x - 1)

Question 14

Find y'', the second derivative, for y = x3-5x2+2

Accepted Answer

6x-10

Question 15

What rule is represented by d/dx (8) = 0?

Accepted Answer

constant rule

Question 16

Find y' for y=sin3(x)tan(4x)

Accepted Answer

sin2(x) [3cos(x)tan(4x) + 4sin(x)sec2(4x)]

Questions 16