Differentiation with Parametric Equations

Differentiation with Parametric Equations

Differentiation Basics

• Understand that differentiation measures the rate of change of a function
• Able to differentiate simple polynomial functions
• Familiar with the power rule for differentiation: if y = ax^n, then dy/dx = nax^(n-1)
• Remeber the constant rule: The derivative of a constant is always zero.

Types of Differentiation

Differential Coefficients

• Understand the meaning of dy/dx, d^2y/dx^2
• Understand how to find higher derivatives

Implicit Differentiation

• Understand what an implicitly defined function is
• Able to apply differentiation in context of implicitly defined functions

Stationary Points

• Understand what stationary points are and able to identify them
• Able to classify stationary points as minimum, maximum or point of inflection
• Use the second derivative to classify stationary points

Convex and Concave Curves

• Understand the difference between concave and convex functions
• Use the second derivative to determine if function is concave or convex
• Able to find points of inflection

Using Differentiation

• Use differentiation to solve problems involving gradients, tangents and normals
• Understand how differentiation can be used to find rates of change
• Use differentiation to find approximate solutions to equations (Newton-Raphson method)

Chain Rule

• Understand the chain rule and when to use it
• Able to differentiate composite functions using the chain rule
• Review examples to solidify understanding of chain rule

Differentiating ex, In x and ax

• Able to differentiate functions with base e and logarithmic functions
• Understand how to differentiate functions with base a

Differentiating sin, cos and tan

• Able to differentiate sine, cosine and tangent functions
• Familiar with the derivatives of these trigonometric functions

Product and Quotient Rules

• Understand and able to use the product rule for differentiation
• Understand and able to use the quotient rule for differentiation

More Differentiation

• Understand how to differentiate functions with roots
• Able to differentiate inverse trigonometric functions
• Confident in differentiating more complex/exotic functions

Differentiation with Parametric Equations

• Understand the concept of parametric equations
• Able to differentiate parametric equations
• Know when and how to use the chain rule in the context of parametric equations