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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.
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.
(b) Find the value of ′(2) and explain the meaning of the answer in the context of the problem. Indicate units of measure. (c) When does the hot air balloon have an acceleration of zero? Justify.
Math 1131 Week 5 Worksheet Name: Discussion Section: Solutions should show all of your work, not just a single nal answer. 3.3: Derivatives of Trigonometric Functions 1.Compute the derivative of each function below using di erentiation rules. (a) f(x) = x3 cosx (b) f(x) = 1 + sinx 1 + cosx (c) f(x) = ex tanx (d) f(x) = secx p x
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.
Answers. Derivatives. Moderate. Trig Functions. xcos ( x ) xsec 2( x ) − tan ( x ) πx2. 1 − cos ( x ) + sin ( x ) 3. 1 + cos 2( x ) − 2cos ( x )
Derivatives of Trigonometric Functions. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the derivative. y = 8. 6 sec x. x. A) y ′ 8 6 tan2x = - + x2. C) y ′ = 8 - 6 sec x tan x x2 B) y ′ 8 = - - 6 csc x x2. 1) ′ D) y = - 8 + 6 sec x tan x x2. 2) y 2 1. = +. sin x cot x.
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.
Derivatives of Trigonometric Functions. Find the derivatives of trigonometric functions: = 4 sin. + 5 cos. = sin. cos. = 2 sec + tan. =. = sin 3 − cos.
Find the derivative: 6. (a) Consider f(x) = x and g(x) = (x + 1)2; then f(g(x)) and g(f(x)) are both decompositions. (b) Every function can be decomposed in multiple ways; for a function f(x), both decompositions given by h(g(x)) and g(h(x) where g(x) = x and h(x) = f(x) are always viable.