Question 1

Find f '(x) where   .

Accepted Answer

The answer of Find f '(x) where   ....

Question 2

Find f '($\theta$) where f($\theta$) = ($\theta$ + sin 2$\theta$)2.

Accepted Answer

2(@#LAT-DLM& + sin 2

Question 3

Let   . Find the slope of the tangent to the graph of f at a general point x0 using limits and find the slope of the tangent at x0 = -3.

Accepted Answer

@#IMG-DLM& = @#IMG-DLM& The sl

Question 4

Find f '(x) where   .

Accepted Answer

The answer of Find f '(x) where   ....

Question 5

Find   if y = (3x2 + 5x) cot x.

Accepted Answer

Question 6

Find the slope of the tangent line to the graph of f(x) = 5x5 - 7 at a general point x0.

Accepted Answer

A)  25x04 - 7 
B)  5x04 
C)  25x04 
D)  5x04 - 1 
E)  5x04 - 7 
A)  25x04 - 7 
B)  5x04 
C)  25x04 
D)  5x04 - 1 
E)  5x04 - 7

Question 7

An air source constantly increases the air supply rate of a balloon. The volume V in cubic feet is given by V(t) = 6t + 1, [0 $\le$ t $\le$ 5], where t is time in seconds. How fast is the volume of the balloon increasing at t = 5s?

Accepted Answer

A)  30 ft3/s 
B)  31 ft3/s 
C)  1 ft3/s 
D)  0 ft3/s 
E)  6 ft3/s 
A)  30 ft3/s 
B)  31 ft3/s 
C)  1 ft3/s 
D)  0 ft3/s 
E)  6 ft3/s

Question 8

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 9

Differentiate   .

Accepted Answer

The answer of Differentiate   ....

Question 10

Find f '(x) where f(x) = (x6 + 6x)11.

Accepted Answer

11(x⁶ + 6

Question 11

Find the points on the graph of y = 2x3 + 21x2 + 60x + 30 at which the tangent is parallel to the x-axis.

Accepted Answer

Equations of tangent that are

Question 12

Find   if   and a is a constant.

Accepted Answer

The answer of Find   if   and...

Question 13

Find   where y = (6x + 3)6(2x + 3)4.

Accepted Answer

36(6x + 3)⁵(2x + 3)⁴ +

Question 14

Find f '(x) if   .

Accepted Answer

The answer of Find f '(x) if   ....

Question 15

Given   , find the slope of the graph of f at x0 = 16.

Accepted Answer

Question 16

Find   if   .

Accepted Answer

The answer of Find   if   ....

Question 17

The position of a moving particle is given by s(t) = 3t5 - 1 where t is time in seconds. The velocity in m/s is given by ds/dt. Find the velocity at t = 3.

Accepted Answer

A)  3,645 m/s 
B)  243 m/s 
C)  405 m/s 
D)  1,215 m/s 
E)  1,214 m/s 
A)  3,645 m/s 
B)  243 m/s 
C)  405 m/s 
D)  1,215 m/s 
E)  1,214 m/s

Question 18

y = cot (sin x). Find dy/dx.

Accepted Answer

A)  cos x csc2 (sin x) 
B)  - cos x csc2 (sin x) 
C)  - sin x csc2 (cos x) 
D)  sin x csc2 (cos x) 
E)  - sin x csc2 (sin x) 
A)  cos x csc2 (sin x) 
B)  - cos x csc2 (sin x) 
C)  - sin x csc2 (cos x) 
D)  sin x csc2 (cos x) 
E)  - sin x csc2 (sin x)

Question 19

y = x4 sin(5x). Find dy/dx.

Accepted Answer

A)  5x4 cos(5x) - 4x3 sin(5x) 
B)  5x4 cos(5x) + x3 sin(5x) 
C)  5x4 cos(5x) + 4x3 sin(5x) 
D)  5x4 cos(5x) 
E)  4x3 sin(5x) 
A)  5x4 cos(5x) - 4x3 sin(5x) 
B)  5x4 cos(5x) + x3 sin(5x) 
C)  5x4 cos(5x) + 4x3 sin(5x) 
D)  5x4 cos(5x) 
E)  4x3 sin(5x)

Question 20

Answer true or false. If y = sin 6x - cos x3, d2y/dx2 = 18 cos x.

Accepted Answer

A) True 
 B)False

Find f '(x) where .

Find f '( $\theta$ ) where f( $\theta$ ) = ( $\theta$ + sin 2 $\theta$ )².

Let . Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent at x₀ = -3.

Find f '(x) where .

Find if y = (3x² + 5x) cot x.

Find the slope of the tangent line to the graph of f(x) = 5x⁵ - 7 at a general point x₀.

An air source constantly increases the air supply rate of a balloon. The volume V in cubic feet is given by V(t) = 6t + 1, [0 $\le$ t $\le$ 5], where t is time in seconds. How fast is the volume of the balloon increasing at t = 5s?

Find if .

Differentiate .

Find f '(x) where f(x) = (x⁶ + 6x)¹¹.

Find the points on the graph of y = 2x³ + 21x² + 60x + 30 at which the tangent is parallel to the x-axis.

Find if and a is a constant.

Find where y = (6x + 3)⁶(2x + 3)⁴.

Find f '(x) if .

Given , find the slope of the graph of f at x₀ = 16.

Find if .

The position of a moving particle is given by s(t) = 3t⁵ - 1 where t is time in seconds. The velocity in m/s is given by ds/dt. Find the velocity at t = 3.

y = cot (sin x). Find dy/dx.

y = x⁴ sin(5x). Find dy/dx.

Answer true or false. If y = sin 6x - cos x³, d²y/dx² = 18 cos x.

Limits and Continuity

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Exam 2: The Derivative

Find f '(x) where .

Find f '( θ\thetaθ ) where f( θ\thetaθ ) = ( θ\thetaθ + sin 2 θ\thetaθ )2.

Let . Find the slope of the tangent to the graph of f at a general point x0 using limits and find the slope of the tangent at x0 = -3.

Find f '(x) where .

Find if y = (3x2 + 5x) cot x.

Find the slope of the tangent line to the graph of f(x) = 5x5 - 7 at a general point x0.

An air source constantly increases the air supply rate of a balloon. The volume V in cubic feet is given by V(t) = 6t + 1, [0 ≤\le≤ t ≤\le≤ 5], where t is time in seconds. How fast is the volume of the balloon increasing at t = 5s?

Find if .

Differentiate .

Find f '(x) where f(x) = (x6 + 6x)11.

Find the points on the graph of y = 2x3 + 21x2 + 60x + 30 at which the tangent is parallel to the x-axis.

Find if and a is a constant.

Find where y = (6x + 3)6(2x + 3)4.

Find f '(x) if .

Given , find the slope of the graph of f at x0 = 16.

Find if .

The position of a moving particle is given by s(t) = 3t5 - 1 where t is time in seconds. The velocity in m/s is given by ds/dt. Find the velocity at t = 3.

y = cot (sin x). Find dy/dx.

y = x4 sin(5x). Find dy/dx.

Answer true or false. If y = sin 6x - cos x3, d2y/dx2 = 18 cos x.

Limits and Continuity

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters

Find f '( $\theta$ ) where f( $\theta$ ) = ( $\theta$ + sin 2 $\theta$ )².

Let . Find the slope of the tangent to the graph of f at a general point x₀ using limits and find the slope of the tangent at x₀ = -3.

Find if y = (3x² + 5x) cot x.

Find the slope of the tangent line to the graph of f(x) = 5x⁵ - 7 at a general point x₀.

An air source constantly increases the air supply rate of a balloon. The volume V in cubic feet is given by V(t) = 6t + 1, [0 $\le$ t $\le$ 5], where t is time in seconds. How fast is the volume of the balloon increasing at t = 5s?

Find f '(x) where f(x) = (x⁶ + 6x)¹¹.

Find the points on the graph of y = 2x³ + 21x² + 60x + 30 at which the tangent is parallel to the x-axis.

Find where y = (6x + 3)⁶(2x + 3)⁴.

Given , find the slope of the graph of f at x₀ = 16.

The position of a moving particle is given by s(t) = 3t⁵ - 1 where t is time in seconds. The velocity in m/s is given by ds/dt. Find the velocity at t = 3.

y = x⁴ sin(5x). Find dy/dx.

Answer true or false. If y = sin 6x - cos x³, d²y/dx² = 18 cos x.