Derivatives Math BootCamp

Question 1

Let h(x)=f(x)/x2. If f(3)=2 and f'(3)=4, then h'(3) is

Accepted Answer

8/27

Question 2

The derivative of the function f(x)=tan(x3) is

Accepted Answer

3x2sec2(x3)

Question 3

If f(x)=sinx then

Accepted Answer

all of the above

Question 4

True or False: If f is differentiable at x, f is continuous at x.

Accepted Answer

True

Question 5

The slope of the line tangent to the graph of x=siny at the point (0,π) is

Accepted Answer

-1

Question 6

If g(x)=sin-1x, then g'(x) is

Accepted Answer

1/√(1-x2)

Question 7

True or False: If f(x)=ln(3x), f'(x)=1/x

Accepted Answer

True

Question 8

True or False: The derivative of f(x)=ln(π) is 1/π.

Accepted Answer

False

Question 9

True or False. The function f(x)=|x| has a derivative at x=0.

Accepted Answer

False

Question 10

If f(x) has an absolute minimum at x=c, then f'(c)=0.

Accepted Answer

False

Question 11

Derivative of ln(e2x)

Accepted Answer

2

Question 12

If f and g are both differentiable and h(x)=f(g(x)), h'(2) equals

Accepted Answer

f'(g(2))g'(2)

Question 13

True or False: If f is not differentiable at x, f is not continuous at x.

Accepted Answer

False

Question 14

If h(x)=f2(x)-g2(x), f'(x)=-g(x), and g'(x)=f(x), then h'(x)=

Accepted Answer

-4f(x)g(x)

Question 15

True or False. If f(x)=x1/3 then f'(0) exists

Accepted Answer

False

Questions 15