Slide 1: Derivatives - Derivative of Function in Parametric Forms
- Introduction to derivatives in parametric forms
- Definition of a parametric equation
- Notation for a parametric equation
- Relationship between a parametric equation and its corresponding set of parametric equations
- Example: Parametric equation of a circle
Slide 2: Derivatives - Special Cases of Derivatives in Parametric Forms
- Derivative of a constant function in parametric form
- Derivative of a linear function in parametric form
- Derivative of a quadratic function in parametric form
- Derivative of a cubic function in parametric form
- Example: Finding the derivative of a parametric equation
Slide 3: Derivatives - Finding Derivatives of Parametric Equations
- Parametric differentiation rule
- Derivative of a parametric equation with respect to the parameter
- Finding dy/dx using the parametric differentiation rule
- Example: Finding dy/dx for a given parametric equation
Slide 4: Derivatives - Implicit Differentiation of Parametric Equations
- Introduction to implicit differentiation
- Applying implicit differentiation to parametric equations
- Finding dy/dx using implicit differentiation
- Example: Finding dy/dx for a parametric equation using implicit differentiation
Slide 5: Derivatives - Second Derivative of Parametric Equations
- Definition of the second derivative
- Finding the second derivative of a parametric equation
- Relation between the second derivatives of x and y with respect to the parameter
- Example: Calculating the second derivative of a given parametric equation
Slide 6: Derivatives - Higher Order Derivatives of Parametric Equations
- Definition of higher order derivatives
- Finding higher order derivatives of parametric equations
- Notation for higher order derivatives
- Example: Calculating the third derivative of a parametric equation
Slide 7: Derivatives - Velocity and Acceleration in Parametric Equations
- Introduction to velocity and acceleration in parametric equations
- Finding velocity using derivatives of parametric equations
- Expressing acceleration in terms of the first and second derivatives of parametric equations
- Example: Finding velocity and acceleration for a given parametric equation
Slide 8: Derivatives - Tangents and Normals to a Parametric Curve
- Definition of tangents and normals to a curve
- Finding the equation of the tangent to a parametric curve
- Finding the equation of the normal to a parametric curve
- Example: Finding the equation of tangent and normal to a given parametric curve
Slide 9: Derivatives - Length of a Parametric Curve
- Introduction to the length of a parametric curve
- Deriving the formula for calculating the length of a parametric curve
- Example: Finding the length of a given parametric curve
Slide 10: Derivatives - Shortest Distance between Two Parametric Curves
- Introduction to finding the shortest distance between two parametric curves
- Deriving the formula for calculating the shortest distance
- Example: Finding the shortest distance between two given parametric curves
Slide 11: Derivatives - Derivative of Function in Parametric Forms
- Introduction to derivatives in parametric forms
- Definition of a parametric equation
- Notation for a parametric equation
- Relationship between a parametric equation and its corresponding set of parametric equations
- Example: Parametric equation of a circle
Slide 12: Derivatives - Special Cases of Derivatives in Parametric Forms
- Derivative of a constant function in parametric form
- Derivative of a linear function in parametric form
- Derivative of a quadratic function in parametric form
- Derivative of a cubic function in parametric form
- Example: Finding the derivative of a parametric equation
Slide 13: Derivatives - Finding Derivatives of Parametric Equations
- Parametric differentiation rule
- Derivative of a parametric equation with respect to the parameter
- Finding dy/dx using the parametric differentiation rule
- Example: Finding dy/dx for a given parametric equation
Slide 14: Derivatives - Implicit Differentiation of Parametric Equations
- Introduction to implicit differentiation
- Applying implicit differentiation to parametric equations
- Finding dy/dx using implicit differentiation
- Example: Finding dy/dx for a parametric equation using implicit differentiation
Slide 15: Derivatives - Second Derivative of Parametric Equations
- Definition of the second derivative
- Finding the second derivative of a parametric equation
- Relation between the second derivatives of x and y with respect to the parameter
- Example: Calculating the second derivative of a given parametric equation
Slide 16: Derivatives - Higher Order Derivatives of Parametric Equations
- Definition of higher order derivatives
- Finding higher order derivatives of parametric equations
- Notation for higher order derivatives
- Example: Calculating the third derivative of a parametric equation
Slide 17: Derivatives - Velocity and Acceleration in Parametric Equations
- Introduction to velocity and acceleration in parametric equations
- Finding velocity using derivatives of parametric equations
- Expressing acceleration in terms of the first and second derivatives of parametric equations
- Example: Finding velocity and acceleration for a given parametric equation
Slide 18: Derivatives - Tangents and Normals to a Parametric Curve
- Definition of tangents and normals to a curve
- Finding the equation of the tangent to a parametric curve
- Finding the equation of the normal to a parametric curve
- Example: Finding the equation of tangent and normal to a given parametric curve
Slide 19: Derivatives - Length of a Parametric Curve
- Introduction to the length of a parametric curve
- Deriving the formula for calculating the length of a parametric curve
- Example: Finding the length of a given parametric curve
Slide 20: Derivatives - Shortest Distance between Two Parametric Curves
- Introduction to finding the shortest distance between two parametric curves
- Deriving the formula for calculating the shortest distance
- Example: Finding the shortest distance between two given parametric curves
Slide 21: Derivatives - Derivative of Function in Parametric Forms
- Introduction to derivatives in parametric forms
- Definition of a parametric equation
- Notation for a parametric equation
- Relationship between a parametric equation and its corresponding set of parametric equations
- Example: Parametric equation of a circle
Slide 22: Derivatives - Special Cases of Derivatives in Parametric Forms
- Derivative of a constant function in parametric form
- Derivative of a linear function in parametric form
- Derivative of a quadratic function in parametric form
- Derivative of a cubic function in parametric form
- Example: Finding the derivative of a parametric equation
Slide 23: Derivatives - Finding Derivatives of Parametric Equations
- Parametric differentiation rule
- Derivative of a parametric equation with respect to the parameter
- Finding dy/dx using the parametric differentiation rule
- Example: Finding dy/dx for a given parametric equation
Slide 24: Derivatives - Implicit Differentiation of Parametric Equations
- Introduction to implicit differentiation
- Applying implicit differentiation to parametric equations
- Finding dy/dx using implicit differentiation
- Example: Finding dy/dx for a parametric equation using implicit differentiation
Slide 25: Derivatives - Second Derivative of Parametric Equations
- Definition of the second derivative
- Finding the second derivative of a parametric equation
- Relation between the second derivatives of x and y with respect to the parameter
- Example: Calculating the second derivative of a given parametric equation
Slide 26: Derivatives - Higher Order Derivatives of Parametric Equations
- Definition of higher order derivatives
- Finding higher order derivatives of parametric equations
- Notation for higher order derivatives
- Example: Calculating the third derivative of a parametric equation
Slide 27: Derivatives - Velocity and Acceleration in Parametric Equations
- Introduction to velocity and acceleration in parametric equations
- Finding velocity using derivatives of parametric equations
- Expressing acceleration in terms of the first and second derivatives of parametric equations
- Example: Finding velocity and acceleration for a given parametric equation
Slide 28: Derivatives - Tangents and Normals to a Parametric Curve
- Definition of tangents and normals to a curve
- Finding the equation of the tangent to a parametric curve
- Finding the equation of the normal to a parametric curve
- Example: Finding the equation of tangent and normal to a given parametric curve
Slide 29: Derivatives - Length of a Parametric Curve
- Introduction to the length of a parametric curve
- Deriving the formula for calculating the length of a parametric curve
- Example: Finding the length of a given parametric curve
Slide 30: Derivatives - Shortest Distance between Two Parametric Curves
- Introduction to finding the shortest distance between two parametric curves
- Deriving the formula for calculating the shortest distance
- Example: Finding the shortest distance between two given parametric curves
Slide 1: Derivatives - Derivative of Function in Parametric Forms Introduction to derivatives in parametric forms Definition of a parametric equation Notation for a parametric equation Relationship between a parametric equation and its corresponding set of parametric equations Example: Parametric equation of a circle