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3.8 Derivatives of Inverse Trigonometric Functions

3.8 Derivatives of Inverse Trigonometric Functions. What you’ll learn about… Derivatives of Inverse Functions Why? The relationship between the graph of a function and its inverse allows us to see the relationship between their derivatives. Derivatives of Inverse Trigonometric functions.

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3.8 Derivatives of Inverse Trigonometric Functions

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  1. 3.8 Derivatives of Inverse Trigonometric Functions What you’ll learn about… Derivatives of Inverse Functions Why? The relationship between the graph of a function and its inverse allows us to see the relationship between their derivatives.

  2. Derivatives of Inverse Trigonometric functions

  3. Calculator Conversions

  4. Where do these come from? Derivative of the arcsine… We can simplify using the identity

  5. Find Use

  6. What about the sec-1x?

  7. Finding the derivative of the Arctangent Using the trig identity

  8. A particle moves along the x-axis so that its position at any time t ≥ 0 is given by x(t) = tan-1(t 2).Find the velocity at the t = 1. Evaluate at t = 1.

  9. What can we do with these derivatives? We can find slopes and write the equations of tangent & normal lines to the curve at x=a! • Find an equation for the line tangent to the graph of y = cot-1x at x = -1 How? • Use the given equation and x=a to find a point on the curve. • Find f ’ and evaluate it at a to get the slope of the tangent. • Recall that -1/a is the slope of the normal line. • Write an equation in point slope form, simplify if needed.

  10. Homework p170 Quick Review 1-10 Exercises 3-27 (3n, nЄI)

  11. Today’s Agenda Correct Homework: Q & A Free Response Practice: No Calculator Homework Page 170 Exercises 15-27 (3n, nЄI), 35-40

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