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16 lis 2022 · Here is a set of practice problems to accompany the Derivatives of Trig Functions section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University.
In this chapter we will expand this list by adding six new rules for the derivatives of the six trigonometric functions: Dxhsin(x)i Dxhtan(x)i Dxhsec(x)i Dxhcos(x)i Dxhcsc(x)i Dxhcot(x)i. This will require a few ingredients. First, we will need the addition formulas for sine and cosine (Equations 3.12 and 3.13 on page 46):
Differentiation - Trigonometric Functions. Date________________ Period____ Differentiate each function with respect to x. 1) f ( x) = sin 2 x3. 3) y = sec 4 x5. 5) y = ( 2 x5 + 3)cos x2. 2) y = tan 5 x3. 4) y = csc 5 x5. −2 x2 − 5. 6) y = cos 2 x3. 7) f ( x) 3 = sin x5. 8) f ( x) = cos ( −3 x2 + 2)2.
3.5 Derivatives of Trig Functions. Problem 1. Suppose we’re given the right triangle below. Express sin( ) and cos( ) in terms of the sides of the triangle. Using the Pythagorean Theorem: Suppose we are given the triangle below. Find the length of the sides A and B. Solution: You might remember this as a 30/60/90 triangle.
Worksheet 13: Trigonometric Derivatives & Chain Rule. Russell Buehler. b.r@berkeley.edu. 1. Find the derivative: (a) y = 2 sec(x) csc(x) y0 = 2 sec(x) tan(x) ( csc(x) cot(x)) y0 = 2 sec(x) tan(x) + csc(x) cot(x) www.xkcd.com. (b) f( ) = sin( ) cos( ) f0( ) = sin( ) sin( ) + cos( ) cos( ) = (c) f( ) = sin( ) csc( ) = sin( ) 1 sin( ) = 1 f0( ) = 0.
Derivatives of Trigonometric Functions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Derivatives of Trigonometric Functions. Solutions should show all of your work, not just a single. nal answer. 1. Compute the derivative of each function below using di erentiation rules. f(x) = x3 cos x. 1 + sin x. f(x) = 1 + cos x. f(x) = ex tan x.
