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ENDURING UNDERSTANDING
FUN3 Recognizing opportunities to apply derivative rules can simplify differentiation.
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Topic Name 
Essential Knowledge 
3.1 The Chain Rule
LEARNING OBJECTIVE FUN3.C Calculate derivatives of compositions of differentiable functions. 
FUN3.C.1 The chain rule provides a way to differentiate composite functions. 
Blog Posts
Foreshadowing the Chain Rule and Power Rule Implies Chain Rule
Experimenting with CAS – Chain Rule (732013) Discovering the Chain Rule
The Chain Rule and another The Chain Rule
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3.2 Implicit Differentiation
LEARNING OBJECTIVE FUN3.D Calculate derivatives of implicitly defined functions.

FUN3.D.1 The chain rule is the basis for implicit differentiation. 
Blog Posts
Implicit Differentiation Approaches to teaching about implicit differentiation
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3.3 Differentiating Inverse Functions
LEARNING OBJECTIVE FUN3.D Calculate derivatives of implicitly defined functions 
FUN3.D.1 The chain rule is the basis for implicit differentiation. 
Blog Posts
The Calculus of Inverses (11122012) Derivatives of the Inverse Trigonometry functions
Implicit Differentiation (9282017) Where to start this topic.
Inverses Graphically and Numerically (11142012) Derivatives of inverses – the hard way and the easy way.
Implicit Differentiation of Parametric Equations (5172014) BC topic.
A Vector’s Derivatives BC topic.
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3.4 Differentiating Inverse Trigonometric Functions
LEARNING OBJECTIVE FUN3.E Calculate derivatives of inverse and inverse trigonometric functions. 
FUN3.E.1 The chain rule and definition of an inverse function can be used to find the derivative of an inverse function, provided the derivative exists. 
Blog Posts
The Calculus of Inverses (11122012) Derivatives of the Inverse Trigonometry functions
Implicit Differentiation (9282017) Where to start this topic.
Inverses Graphically and Numerically (11142012) Derivatives of inverses – the hard way and the easy way.
Implicit Differentiation of Parametric Equations (5172014) BC topic.
A Vector’s Derivatives BC topic.
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3.5 Selecting Procedures for Calculating Derivatives
LEARNING OBJECTIVE 
None 
Blog Posts
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3.6 Calculating HigherOrder Derivatives
LEARNING OBJECTIVE FUN3.F Determine higher order derivatives of a function 
FUN3.F.1 Differentiating f ′ produces the second derivative f ″, provided the derivative of f ′ exists; repeating this process produces higher order derivatives of f . 
FUN3.F.2 Higherorder derivatives are represented with a variety of notations. For ,notations for the second derivative include , and . Higherorder derivatives can be denoted or 
Blog Posts