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Basic Derivatives The Math Center Tutorial Services Brought To You By:

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► Algebraically, the ► Geometrically as the slope of the tangent line to the graph of at ► Functionally as the instantaneous rate of change of at Definition Of A Derivative The derivative of a function at a point x=a, can be interpreted in several different ways:

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Applications of Derivatives ► Finding the instantaneous velocity of an object at a precise moment in time ► Finding the instantaneous rate of change of a function ► Finding the slope of the tangent to the graph of a function * NOTE: the derivative symbol can be written as or or

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Basic Derivative Formulas ► If, where n is a constant, then ► If, where c is a constant, then Power Rule Constant Rule Power Rule

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If, then More basic derivative formulas Logarithm Rule Exponential Rule

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Examples Solution: Following the Power Rule, we can now calculate the derivative. we can now calculate the derivative. Differentiate:

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Examples (cont.) Solution: Following the Constant Rule, we can now calculate the derivative. Differentiate:

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Examples (cont.) Solution: Following the Power Rule, we can now calculate the derivative. Differentiate:

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Examples (cont.) Solution: Following the Logarithm Rule, we can now calculate the derivative. Differentiate: u = x u’ = 1

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Examples (cont.) Solution: Following the Exponential Rule, we can now calculate the derivative. Differentiate:

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Questions???

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Helpful Links ► Derivatives and Integrals Handout Derivatives and Integrals Handout Derivatives and Integrals Handout ► Implicit Differentiation Handout Implicit Differentiation Handout Implicit Differentiation Handout ► Derivatives Student Handout Derivatives Student Handout Derivatives Student Handout ► Derivatives Quiz Derivatives Quiz Derivatives Quiz

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