Basic Derivatives

Question 1

Find the average rate of change of the function over the given interval.

Accepted Answer

-2

Question 2

Find f'(x).

Accepted Answer

f'(x) = (5x4 + 1)(-15x4) + (-3x5 - 4)(20x3)

Question 3

Uh-oh. Where is this function NOT differentiable?

Accepted Answer

At x = 1.

Question 4

Find the instantaneous rate of change of the function at the given value.

Accepted Answer

2

Question 5

Find y'.

Accepted Answer

y' = 2

Question 6

A derivative is also ________________

Accepted Answer

the instantaneous velocity., the slope., the instantaneous rate of change.

Question 7

Find y'.

Accepted Answer

y' = (-2x5)(5x4) + (x5 - 2)(-10x4), y' = -100x9 +20x4

Question 8

Find the equation of the TANGENT line to the function at the given point.

Accepted Answer

y = 8x +19

Question 9

Find the average rate of change of the function over the given interval.

Accepted Answer

-3

Question 10

Find y'.

Accepted Answer

y' = (x5 - 4x4 - 1)(-10x4) + (-2x5 +1)(5x4 - 16x3)

Question 11

Find the derivative at the given value.

Accepted Answer

f'(3) = 4

Question 12

Find y'.

Accepted Answer

y' = -12x3

Question 13

Find f'(x).

Accepted Answer

f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)2, f'(x) = -(5x4)(2x5 + 2)-2(10x4) + (2x5 + 1)-1(20x3)

Question 14

Find the instantaneous rate of change of the function at the given value.

Accepted Answer

5

Question 15

Find the derivative at the given value.

Accepted Answer

f'(-1) = 9

Question 16

The original function, for example s(t), is the ____________

Accepted Answer

position function.

Question 17

Find y'

Accepted Answer

y' = (-3x4 - 5)(-20x3) + (-5x4 + 1)(-12x3), y' = 120x7 - 36x2 +100

Question 18

Find the derivative at the given value.

Accepted Answer

f'(3) = 3

Question 19

Find the average rate of change of the function over the given interval.

Accepted Answer

-1

Question 20

Find the equation of the TANGENT line to the function at the given point.

Accepted Answer

y = 5x -1

Question 21

The derivative is the _____________

Accepted Answer

instantaneous velocity.

Question 22

Find dy/dx.

Accepted Answer

dy/dx = -(4x3 +2x2)(3x2 + 3)-2(6x) + (3x2 + 3)-1(12x2), dy/dx = [(3x2 + 3)(12x2 +4x) - (4x3 +2x2)(6x)] / (3x2 + 3)2

Questions 22