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Chapter 3 The Derivative

Chapter 3 The Derivative. Tangent line The derivative at a certain point Instantaneous rate of change General rates of change Average and instantaneous rates of change Secant lines The slope between two points of a graph Average rate of change Definition of the derivative Product rule

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Chapter 3 The Derivative

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  1. Chapter 3The Derivative

  2. Tangent line • The derivative at a certain point • Instantaneous rate of change • General rates of change • Average and instantaneous rates of change • Secant lines • The slope between two points of a graph • Average rate of change • Definition of the derivative • Product rule • Quotient rule

  3. Derivatives of Trig functions • Cos(x)= -sin(x) • Sin(x)=cos(x) • Csc(x)= -cot(x)csc(x) • Sec(x)=tan(x)sec(x) • Power rule • Chain rule • Second and third derivative • Take the derivative of the derivative

  4. Tangent Line • The derivative at a certain point • Instantaneous rate of change

  5. General Rates of Change • Average and instantaneous rates of change • Average is the slope between two points • Instantaneous is the slope at a single point

  6. Secant Line • The slope between two points of a graph • Average rate of change

  7. Definition of the Derivative

  8. Product Rule

  9. Quotient Rule

  10. Derivatives of Trig Functions • Cos(x)= -sin(x) • Sin(x)=cos(x) • Csc(x)= -cot(x)csc(x) • Sec(x)=tan(x)sec(x)

  11. Power Rule

  12. Chain Rule

  13. Second and Third Derivative • Take the derivative of the derivative

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