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Chapter 3 – Differentiation Rules

Chapter 3 – Differentiation Rules. 3.3 Derivatives of Trig Functions. Remember…. *This functions represents the inverse sin of x ( arcsin x ) and not any of the other listed functions. Definitions. Derivative: Sine.

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Chapter 3 – Differentiation Rules

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  1. Chapter 3 – Differentiation Rules 3.3 Derivatives of Trig Functions Section 3.3 Derivatives of Trig Functions

  2. Remember… *This functions represents the inverse sin of x (arcsinx) and not any of the other listed functions. Section 3.3 Derivatives of Trig Functions

  3. Definitions Section 3.3 Derivatives of Trig Functions

  4. Derivative: Sine • If we sketch the graph of the function f(x) = sin x and use the interpretation of f (x) as the slope of the tangent to the sine curve in order to sketch the graph of f , then it looks as if the graph of f  may be the same as the cosine curve. Section 3.3 Derivatives of Trig Functions

  5. Example Prove that the derivative of sin(x) = cos(x). Section 3.3 Derivatives of Trig Functions

  6. Derivatives of the Trig Functions TriggyRulesby Matheatre D’riv-ativeof Sine X, is Cosine X. Derivative of Secant X is, Amazing! Secant X Tan X! Driv-ative Tangent X: Secant Squared X. Remember the Chain rule, Chain Rule! Don’t forget the dx, dx! Triggyrules, triggy rules, Triggy, triggy, trigg rules, Triggy rules, triggy rules, Triggy, triggy, trigg rules, Y’knowtrig don’t choke. Derivatives of co-functions are- All Negative. Ya substitute the functions for the co-functions as implied. I said y’know trig don’t choke, Derivatives of co-functions are- All Negative. Ya substitute the functions for the co-functions as implied. Section 3.3 Derivatives of Trig Functions

  7. Derivatives of the Trig Functions Section 3.3 Derivatives of Trig Functions

  8. Example 1 Find the derivative of the following function: Section 3.3 Derivatives of Trig Functions

  9. Example 2 Find the derivative of the following function: Section 3.3 Derivatives of Trig Functions

  10. Example 3 Find if f (x) = sec x Section 3.3 Derivatives of Trig Functions

  11. Example 4 • On a sunny day, a 50-ft flagpole casts a shadow that changes with the elevation of the sun. Let s be the length of the shadow and  the angle of elevation of the sun. Find the rate at which the length of the shadow is changing with respect to  when =45o. Express your answer in units of ft/degree. Section 3.3 Derivatives of Trig Functions

  12. Example 5 As illustrated on the left, suppose a spring with an attached mass is stretched 3 cm beyond its rest position and released at time t = 0. Assuming that the position function of the top of the attached mass is s = -3cost where s is in cm and t is in seconds, find the velocity function and discuss the motion of the attached mass. Section 3.3 Derivatives of Trig Functions

  13. Example 6 Find the equation of the normal and tangent lines to the curve at the given point. Section 3.3 Derivatives of Trig Functions

  14. Example 7 Find the limit Section 3.3 Derivatives of Trig Functions

  15. Example 8 Differentiate. Section 3.3 Derivatives of Trig Functions

  16. Assignment • Page 154 #1-25 odd, 39-49 odd Section 3.3 Derivatives of Trig Functions

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