Learning Objective 2.1C

Learning Objective 2.1C Students will be able to calculate derivatives.

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We've been solving derivatives using a variety of methods, with the constant promise that soon you will learn shortcuts to make your life easier. Now its time to learn these shortcuts. Then you'll learn how to solve more complicated derivatives.

EK 2.1C1 Shows you the experience of finding derivatives without the shortcuts

EK 2.1C2 Shows you the shortcuts

EK 2.1C3 Shows you how to use shortcuts on derivatives that have multiple terms

EK 2.1C4 Shows you the chain rule, and how to use it for composite functions

EK 2.1C5 Shows you how to use the chain rule for implicit differentiation

EK 2.1C6 Shows you how to use the chain rule for inverse functions

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Essential Knowledge 2.1C1 Students will know that direct application of the definition of the derivative can be used to find the derivative for selected functions, including polynomial, power, sine, cosine, exponential, and logarithmic functions.

Essential Knowledge 2.1C2 Students will know that specific rules can be used to calculate derivatives for classes of functions, including polynomial, rational, power, exponential, logarithmic, trigonometric, and inverse trigonometric.

Essential Knowledge 2.1C3 Students will know that sums, differences, products, and quotients of functions can be differentiated using derivative rules.

Essential Knowledge 2.1C4 Students will know that the chain rule provides a way to differentiate composite functions.

Essential Knowledge 2.1C5 Students will know that the chain rule is the basis for implicit differentiation.

Essential Knowledge 2.1C6 Students will know that the chain rule can be used to find the derivative of an inverse function, provided the derivative of that function exists.