Chain, Product and Quotient Rules
Composite, product and quotient functions are differentiated by the chain rule, the product rule and the quotient rule respectively.
What is Chain, Product and Quotient Rules?
Composite, product and quotient functions are differentiated by the chain rule, the product rule and the quotient rule respectively.
Key formula / rule: The chain rule multiplies the outer derivative by the inner derivative.
Key points
- Apply the chain rule to nested composite functions.
- Compute derivatives of products and quotients of standard functions.
Common exam trap
Forgetting the inner derivative in a composite function.
Definitions
- Term
Chain, Product and Quotient Rules
- Meaning
Composite, product and quotient functions are differentiated by the chain rule, the product rule and the quotient rule respectively.
- Term
Chain, Product and Quotient Rules — explanation
- Meaning
Almost every examination derivative is a composite of standard functions, so recognising the outer and inner functions correctly is the whole task. The rules compose, so nested applications are routine.
Learning objectives
Apply the chain rule to nested composite functions.
Compute derivatives of products and quotients of standard functions.
Formulae
- Key point
The chain rule multiplies the outer derivative by the inner derivative.
- Key point
The product rule is u'v + uv', not u'v'.
- Key point
The quotient rule numerator order matters: u'v - uv'.
Prerequisites
MAT-U2-LC-T1-S2-C2
Common mistakes
Forgetting the inner derivative in a composite function.
Reversing the numerator terms in the quotient rule.
Keywords
Chain
Product
Quotient
Rules
Practice preview
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