Differentiation Flashcards
Limit of functions at a point
Highest Lower Bound
Infimum
Limit of functions at a point
Smallest Upper Bound
Supremum
Limit of functions at a point
The limit of sinx / x at 0
= 1
Rules of derivates
Constant rule
Rules of derivates
Constant Multiple Rule
Rules of derivatives
Power Rule
Rules of derivatives
Sum and Difference Rule
Rules of derivatives
Product Rule
Rules of derivatives
Quotient Rule
Rules of derivatives
Chain Rule
Rules of derivatives
Extended Chain Rule (3 elements)
How to find the equation of the tangent (parallel) given an x value?
- Find the derivative of the equation (dy/dx)
- Find the y value by plugging x to the original equation
- Find the gradient by substituting x values with the respective x coordinate
- Use slope-intercept or point-slope formula to find equation
How to find the equation of the normal (perpendicular) given an x value?
- Find the derivative of the equation (dy/dx)
- Find y value by plugging in x to original equation
- Find the gradient by substituting x values with the respective x coordinate
- Find the opposite reciprocal of the gradient
- Use slope-intercept or point-slope form to find equation
Derivatives of common functions
Derivative of log and ln
Derivatives of common functions
Derivative of trigonometric functions
Derivatives of common functions
Derivative of Euler’s number to the x power
Derivatives of common functions
Derivative of 1/x
-1/x^2
Derivatives of common functions
Derivative of square root of x
Method to solve small increments
- Find the derivative of the equation
- Use the concept that dy/dx = change(y)/change(x)
- Substitute the amount of change in x
- Substitute x into the derivative
- Solve for the change in y
Small increments
dy/dx = change (y) / change (x)
Connected rates of change: find dA/dt
Volume of a sphere
Area of a circle with radius
Circumference of a circle
Volume of a cylinder
Surface area of a sphere
Surface area of a cylinder
