'Du dx' presentation slideshows

Chapter Two

Chapter Two. Derivatives and Their Uses. Limit as x?3 Shown Graphically. Derivative : ??. (1) x takes values closer and closer to 3 but never equaling 3 lim ( x ?3) (2x+4)=10 lim ( x ? c ) f(x) lim ( x ? c - ) f(x) ??? lim ( x ? c + ) f(x) ???.

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When we talk about the function f defined for all real numbers x by

DERIVATIVES OF TRIGONOMETRIC FUNCTIONS. When we talk about the function f defined for all real numbers x by , it is understood that means the sine of the angle whose radian measure is . A similar convention holds for the other trigonometric functions cos , tan, csc , sec, and cot.

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DRAG E X A M P L E S

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Sec. 5.8 Inverse Trig Functions and Differentiation

Sec. 5.8 Inverse Trig Functions and Differentiation. By Dr. Julia Arnold. Since a function must pass the horizontal line test to have an inverse function, the trig functions, being periodic, have to have their domains restricted in order to pass the horizontal line test.

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=

=. (7x+2) 13 /13 (7x+2) 13 /13 + C (7x+2) 11 /13 + C (7x+2) 11 /11 + C. u = 2x-3 du/ dx = 2 du = 2 dx du/2 = dx. Power Rule. If u is any differentiable function and n is not -1, then. Let u = the bad stuff. Using the power rule u = 1 + z 2 .

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AP Calculus BC Monday, 27 January 2014

AP Calculus BC Monday, 27 January 2014. OBJECTIVE TSW (1) explore properties of inverse trigonometric functions, (2) differentiate inverse trig functions, and (3) review basic differentiation rules. Everything on the schedule is pushed back one day. ASSIGNMENTS DUE Sec. 6.2 ? wire basket

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Inverse Trig Functions and Differentiation

Inverse Trig Functions and Differentiation. By Dr. Julia Arnold. Since a function must pass the horizontal line test to have an inverse function, the trig functions, being periodic, have to have their domains restricted in order to pass the horizontal line test.

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Stress-Strain Theory

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Drill

Drill. Let f(x) = sin(x) and g(x) = 1+ x 2 and h(x) = 7x f(g(x)) = g(h(x)) = f(g(h(x)) h(g(x)). Chain Rule. Lesson 3.6. Objectives. Students will be able to differentiate composite functions using the Chain Rule. find slopes of parameterized curves. Relating Derivatives.

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CHAIN RULE

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AP Calculus BC Wednesday, 19 February 2014

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AP Calculus BC Monday , 18 November 2013

AP Calculus BC Monday , 18 November 2013. OBJECTIVE TSW use integration by subsitution . ASSIGNMENT DUE Sec. 4.1 ? wire basket Tests are graded. Look on line for your score. Due to time constraints, we will not go over them in class.

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SHORTCUTS TO DERIVATIVES

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Integration by Parts

Integration by Parts. Summary of Common Integrals Using Integration by Parts. 1. For integrals of the form. Let u = x n and let dv = e ax dx, sin ax dx, cos ax dx. 2. For integrals of the form. Let u = lnx, arcsin ax, or arctan ax and let dv = x n dx. 3. For integrals of the form. or.

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Integration by parts

Integration by parts. Product Rule:. Integration by parts. Let dv be the most complicated part of the original integrand that fits a basic integration Rule (including dx ). Then u will be the remaining factors. OR. Let u be a portion of the integrand whose

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5.7 Inverse Trigonometric Functions: Integration and Completing the Square

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Lesson 3-6

Lesson 3-6. Implicit Differentiation. Objectives. Use implicit differentiation to solve for dy/dx in given equations Use inverse trig rules to find the derivatives of inverse trig functions. Vocabulary.

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5.4 Exponential Functions: Differentiation and Integration

5.4 Exponential Functions: Differentiation and Integration. The inverse of f(x) = ln x is f -1 = e x. Therefore, ln (e x ) = x and e ln x = x. Solve for x in the following equations. Take the ln of both sides. Operations with Exponential Functions.

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Chain Rule Round Robin

Chain Rule Round Robin. Seat A: find U and du / dx Seat B: find y in terms of u and dy / du Seat C: find dy / dx Seat D: Simplify dy / dx. Seat B: find U and du / dx Seat C: find y in terms of u and dy / du Seat D: find dy / dx Seat A: Simplify dy / dx.

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