Question 1

A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sold as aphrodisiacs. After severe conservation measures are implemented, it is hoped that the turtle population will grow according to the rule   , where  denotes the population at the end of year  . ​
Find the rate of growth of the turtle population when  .
​

Accepted Answer

The answer of A certain species of turtle faces extinction...

Question 2

Find the derivative of the function f by using the rules of differentiation. ​  ​

Accepted Answer

The derivative of a constant is 0. 
The derivative of x is 1. 
The derivative of e^x is e^x. 
Using these rules, we can easily differentiate the given function:

f(x) = 3 - 4x + 2e^x

f'(x) = 0 - 4 + 2e^x

f'(x) = -4 + 2e^x

Therefore, the correct choice is B.

Question 3

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Question 4

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Question 5

Find the slope and an equation of the tangent line to the graph of the function f at the specified point. ​  ;  ​

Accepted Answer

The answer of Find the slope and an equation of...

Question 6

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 7

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Question 8

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 9

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Question 10

Let  . ​
Find the values of  for which  .
​

Accepted Answer

The answer of Let  . ​
Find the values of...

Question 11

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 12

Find the limit by evaluating the derivative of a suitable function at an appropriate point. (Hint: Look at the definition of the derivative.)

Accepted Answer

The answer of Find the limit by evaluating the derivative...

Question 13

An economy's consumer price index (CPI) is described by the function   , where  corresponds to 1995. ​
At what rate was the CPI changing in 1998?
​

Accepted Answer

The answer of An economy's consumer price index (CPI) is...

Question 14

If f is differentiable, then  .

Accepted Answer

This is a direct consequence of the chain rule of differentiation. If f is differentiable, then g = 11f is differentiable, and we have (g)'(x) = 11f'(x) for all x.

Question 15

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Question 16

If f is differentiable, then  .

Accepted Answer

The answer of If f is differentiable, then  ....

Question 17

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 18

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Question 19

Find the derivative of the function.
​

Accepted Answer

The answer of Find the derivative of the function.
​ ...

Question 20

Find the derivative of the function by using the rules of differentiation. ​  ​

Accepted Answer

The answer of Find the derivative of the function by...

Quiz 3: Differentiation

Find the derivative of the function f by using the rules of differentiation.

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function by using the rules of differentiation.

Find the slope and an equation of the tangent line to the graph of the function f at the specified point. ;

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Let . Find the values of for which .

Find the derivative of the function.

Find the limit by evaluating the derivative of a suitable function at an appropriate point. (Hint: Look at the definition of the derivative.)

An economy's consumer price index (CPI) is described by the function , where corresponds to 1995. At what rate was the CPI changing in 1998?

If f is differentiable, then .

Find the derivative of the function by using the rules of differentiation.

If f is differentiable, then .

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Quiz 3: Differentiation

Find the derivative of the function f by using the rules of differentiation. ​ ​

Find the derivative of the function by using the rules of differentiation. ​ ​

Find the derivative of the function by using the rules of differentiation. ​ ​

Find the slope and an equation of the tangent line to the graph of the function f at the specified point. ​ ; ​

Find the derivative of the function. ​

Find the derivative of the function by using the rules of differentiation. ​ ​

Find the derivative of the function. ​

Find the derivative of the function by using the rules of differentiation. ​ ​

Let . ​ Find the values of for which . ​

Find the derivative of the function. ​

Find the limit by evaluating the derivative of a suitable function at an appropriate point. (Hint: Look at the definition of the derivative.)

An economy's consumer price index (CPI) is described by the function , where corresponds to 1995. ​ At what rate was the CPI changing in 1998? ​

If f is differentiable, then .

Find the derivative of the function by using the rules of differentiation. ​ ​

If f is differentiable, then .

Find the derivative of the function. ​

Find the derivative of the function by using the rules of differentiation. ​ ​

Find the derivative of the function. ​

Find the derivative of the function by using the rules of differentiation. ​ ​

Find the derivative of the function f by using the rules of differentiation.

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function by using the rules of differentiation.

Find the slope and an equation of the tangent line to the graph of the function f at the specified point. ;

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Let . Find the values of for which .

Find the derivative of the function.

An economy's consumer price index (CPI) is described by the function , where corresponds to 1995. At what rate was the CPI changing in 1998?

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.

Find the derivative of the function.

Find the derivative of the function by using the rules of differentiation.