Differentiation

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New Textbook

• Sine & Cosine From First Principles
• Differentiating Logs & Exponentials
• dx/dy
• Chain Rule
• Product Rule
• Quotient Rule
• Other Trig Derivatives
• Parametric Equations
• Implicit Differentiation
• Concave & Convex Functions
• Connected Rates of Change (Chain Rule in Context)

Old Textbook(ish)

• Differentiating Logs & Exponentials
• Chain Rule
• Product Rule
• Quotient Rule
• Sine & Cosine From First Principles
• Other Trig Derivatives
• dx/dy
• Parametric Equations
• Implicit Differentiation
• Concave & Convex Functions
• Connected Rates of Change (Chain Rule in Context)

*note the old textbook actually introduces Logs and Exponentials AFTER the Quotient rule, but I have structured like this to maximise the use of resources.

WW Approach

• Derivatives of ALL Trig & exponentials without proof
• Chain Rule
• Product Rule
• Quotient Rule
• Parametric Equations
• dx/dy
• Implicit Differentiation
• First Principles for Sine & Cosine. Deriving other Trig with Chain and Quotient Rule.
• Concave & Convex Functions
• Connected Rates of Change (Chain Rule in Context)

Pros:

• More Textbook Resources

Cons:

• Some concepts practiced before fully elaborated (chain rule within Sine, Cosine, Logs & exponentials)
• Limited Past Paper Questions to support early concepts (Pre Chain, Product & Quotient Rules)

Pros:

• Old Textbook Resources
• No concept practiced before fully explained

Cons:

• Trig derivatives introduced last, limiting practise time and familiarisation before integration

Pros:

• All derivatives introduced first, maximising time to practise within each of the Chain, Product and Quotient rules.
• Supports recognition of derivatives ahead of integration chapter.

Cons:

• Limited Resources for early stages – memorisation activities mainly
• All derivatives introduced before fully explained where they come from.
• No textbook resources