Differentiation

Question 1

Limit of functions at a point

Highest Lower Bound

Answer 1

Infimum

Question 2

Limit of functions at a point

Smallest Upper Bound

Answer 2

Supremum

Question 3

Limit of functions at a point

The limit of sinx / x at 0

Answer 3

= 1

Question 4

Rules of derivates

Constant rule

Answer 4

Question 5

Rules of derivates

Constant Multiple Rule

Answer 5

Question 6

Rules of derivatives

Power Rule

Answer 6

Question 7

Rules of derivatives

Sum and Difference Rule

Answer 7

Question 8

Rules of derivatives

Product Rule

Answer 8

Question 9

Rules of derivatives

Quotient Rule

Answer 9

Question 10

Rules of derivatives

Chain Rule

Answer 10

Question 11

Rules of derivatives

Extended Chain Rule (3 elements)

Answer 11

Question 12

How to find the equation of the tangent (parallel) given an x value?

Answer 12

1. Find the derivative of the equation (dy/dx)
2. Find the y value by plugging x to the original equation
3. Find the gradient by substituting x values with the respective x coordinate
4. Use slope-intercept or point-slope formula to find equation

Question 13

How to find the equation of the normal (perpendicular) given an x value?

Answer 13

1. Find the derivative of the equation (dy/dx)
2. Find y value by plugging in x to original equation
3. Find the gradient by substituting x values with the respective x coordinate
4. Find the opposite reciprocal of the gradient
5. Use slope-intercept or point-slope form to find equation

Question 14

Derivatives of common functions

Derivative of log and ln

Answer 14

Question 15

Derivatives of common functions

Derivative of trigonometric functions

Answer 15

Question 16

Derivatives of common functions

Derivative of Euler’s number to the x power

Answer 16

Question 17

Derivatives of common functions

Derivative of 1/x

Answer 17

-1/x^2

Question 18

Derivatives of common functions

Derivative of square root of x

Answer 18

Question 19

Method to solve small increments

Answer 19

1. Find the derivative of the equation
2. Use the concept that dy/dx = change(y)/change(x)
3. Substitute the amount of change in x
4. Substitute x into the derivative
5. Solve for the change in y

Question 20

Small increments

Answer 20

dy/dx = change (y) / change (x)

Question 21

Connected rates of change: find dA/dt

Answer 21

Question 22

Volume of a sphere

Answer 22

Question 23

Area of a circle with radius

Answer 23

Question 24

Circumference of a circle

Answer 24

Question 25

Volume of a cylinder

Answer 25

Question 26

Surface area of a sphere

Answer 26

Question 27

Surface area of a cylinder

Answer 27