Chain Rule & Implicit Differentiation

 

The Chain Rule

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Chain Rule for derivatives, including definition of composite functions and a worked example.

Two part question that involves applying and explaining the chain rule for derivatives.

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Implicit Differentiation

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Implicit differentiation defined.

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Finding the derivative of the inverse sine function using implicit differentiation.

Finding the derivative of an implicitly defined function.

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Example of Implicit Differentiation

Implicit differentiation demonstrated through an example.

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Derivatives of Combinations of Functions

Rules for the derivatives of sums and products of functions, as well as the chain rule and rules for finding the derivative of an inverse function.

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Continuously Compounded Interest

Two part question involving a bank's liability from a loan and a savings account, each with continuously compounded interest.

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Derivatives of Exponential and Trigonometric Functions

Taking the first and second derivatives of a function involving an exponential and a cosine.

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Implicit Differentiation and Tangent Line to a Graph

Finding the equation of a tangent line to the graph of a function that is defined with an implicit equation.

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Evaluating Derivatives

Two questions finding the derivatives of functions.

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Chain Rule and Implicit Differentiation

Eight questions which involve finding derivatives using the Chain rule and the method of implicit differentiation.

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