Exam2: Differentiation

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Presentation transcript:

Exam2: Differentiation Exam-2 Problems Differentiability Differentiation Position function Find limit Differentiation: Direct: Find the g’(2) Indirect: Find the slope of the tangent line, normal line, rate of change, parallel to the line Find slope in different ways Find Find f’(x) Vertical or horizontal tangent others

Exam2: Differentiation Derivative Quotient Rule Derivative of exponential Derivative Product Rule DERIVATIVES OF TRIGONOMETRIC FUNCTIONS: Implicit diff. Chain Rule:

Chapter3: Differentiation Exam-2 Problems The slope of the tangent line The slope of the normal line The rate of change

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Sec 3.7: Implicit Differentiation

Chapter3: Differentiation

Sec 3.7: Implicit Differentiation

Sec 3.7: Implicit Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation Exam-2 Problems Direct: Find the g’(2) Indirect: Find the slope…. Find slope in different ways Find Find: lim Find f’(x) others (Sketch and find the slopes)

Sec 3.9: Inverse Trigonometric Functions

Sec 3.9: Inverse Trigonometric Functions

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Exam2: Differentiation HOW CAN A FUNCTION FAIL TO BE DIFFERENTIABLE? Definition: the curve has a vertical tangent line when x = a 1) f is cont at a 2)

Chapter3: Differentiation

Chapter3: Differentiation TERM-121 Exam-2

Chapter3: Differentiation TERM-121 Exam-2

Chapter3: Differentiation TERM-121 Exam-2

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation Exam-2 Problems Direct: Find the g’(2) Indirect: Find the slope…. Find slope in different ways Find Find: lim Find f’(x) others

Sec 3.5: Derivatives Of Trigonometric Functions

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation Exam-2 Problems Direct: Find the g’(2) Indirect: Find the slope…. Find slope in different ways Find Find: lim Find f’(x) others

Chapter3: Differentiation

Chapter3: Differentiation

Sec 3.5: Derivatives Of Trigonometric Functions

Sec 3.5: Derivatives Of Trigonometric Functions

Sec 3.5: Derivatives Of Trigonometric Functions

Chapter3: Differentiation Exam-2 Problems Direct: Find the g’(2) Indirect: Find the slope…. Find slope in different ways Find Find: lim Find f’(x) others

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation

Chapter3: Differentiation TERM-121 Exam-2

Chapter3: Differentiation

Chapter3: Differentiation Exam-2 Problems Direct: Find the g’(2) Indirect: Find the slope…. Find slope in different ways Find Find: lim Find f’(x) Others ,

Chapter3: Differentiation

Chapter3: Differentiation

Sec 3.11: Linearization and Differentials

Sec 3.11: Linearization and Differentials

Sec 3.11: Linearization and Differentials

Sec 3.5: Implicit Differentiation

Sec 3.5: Implicit Differentiation

Sec 3.5: Implicit Differentiation

Sec 3.5: Implicit Differentiation

Chapter3: Differentiation

Sec 3.7: Implicit Differentiation

Chapter3: Differentiation

Sec 3.7: Implicit Differentiation