 3.4.1: Differentiate.
 3.4.2: Differentiate.
 3.4.3: Differentiate.
 3.4.4: Differentiate.
 3.4.5: Differentiate.
 3.4.6: Differentiate.
 3.4.7: Differentiate.h csc e cos u cu cot tt t tt
 3.4.8: Differentiate.y e u h csc e cos u cu cot tt
 3.4.9: Differentiate.y x cos x 9
 3.4.10: Differentiate.y 1 sin x x cos x y
 3.4.11: Differentiate.f sec 1 sec y 1
 3.4.12: Differentiate.y tan x 1 sec x f
 3.4.13: Differentiate.y y sin x x 2
 3.4.14: Differentiate.y csc cot sin x
 3.4.15: Differentiate.y sec tan y
 3.4.16: Differentiate.y x sin x cos x
 3.4.17: Prove that ddx csc x csc x cot x .
 3.4.18: Prove that ddx sec x sec x tan xd .
 3.4.19: Prove that ddx cot x csc2xd.
 3.4.20: Prove, using the definition of derivative, that if , then .
 3.4.21: Find an equation of the tangent line to the curve at the given poin...
 3.4.22: Find an equation of the tangent line to the curve at the given poin...
 3.4.23: Find an equation of the tangent line to the curve at the given poin...
 3.4.24: Find an equation of the tangent line to the curve at the given poin...
 3.4.25: (a) Find an equation of the tangent line to the curve at the point ...
 3.4.26: (a) Find an equation of the tangent line to the curve at the point ...
 3.4.27: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 3.4.28: (a) If , find . ; (b) Check to see that your answer to part (a) is ...
 3.4.29: For what values of does the graph of have a horizontal tangent?
 3.4.30: Find the points on the curve at which the tangent is horizontal.
 3.4.31: A mass on a spring vibrates horizontally on a smooth level surface ...
 3.4.32: An elastic band is hung on a hook and a mass is hung on the lower e...
 3.4.33: A ladder 10 ft long rests against a vertical wall. Let be the angle...
 3.4.34: An object with weight is dragged along a horizontal plane by a forc...
 3.4.35: Find the limit.lim xl0 sin 3x x
 3.4.36: Find the limit.lim xl0 sin 4x sin 6x
 3.4.37: Find the limit.lim tl0 tan 6t sin 2t
 3.4.38: Find the limit.lim l0 cos 1 sin li
 3.4.39: Find the limit.lim l0 sincos sec li
 3.4.40: Find the limit.lim tl0 sin2 3t t 2
 3.4.41: Find the limit.lim xl0 cot 2x csc x
 3.4.42: Find the limit.lim x l 4 sin x cos x cos 2x
 3.4.43: Find the limit.lim l0 sin tan
 3.4.44: Find the limit.lim xl1 sinx 1 x 2 x 2 li
 3.4.45: Differentiate each trigonometric identity to obtain a new (or famil...
 3.4.46: A semicircle with diameter sits on an isosceles triangle to form a ...
 3.4.47: The figure shows a circular arc of length and a chord of length , b...
Solutions for Chapter 3.4: Derivatives of Trigonometric Functions
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 3.4: Derivatives of Trigonometric Functions
Get Full SolutionsChapter 3.4: Derivatives of Trigonometric Functions includes 47 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 47 problems in chapter 3.4: Derivatives of Trigonometric Functions have been answered, more than 45393 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Calculus, was written by and is associated to the ISBN: 9780534393397.

Coterminal angles
Two angles having the same initial side and the same terminal side

Ellipsoid of revolution
A surface generated by rotating an ellipse about its major axis

Exponential decay function
Decay modeled by ƒ(x) = a ? bx, a > 0 with 0 < b < 1.

Graph of parametric equations
The set of all points in the coordinate plane corresponding to the ordered pairs determined by the parametric equations.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Infinite discontinuity at x = a
limx:a + x a ƒ(x) = q6 or limx:a  ƒ(x) = q.

Law of cosines
a2 = b2 + c2  2bc cos A, b2 = a2 + c2  2ac cos B, c2 = a2 + b2  2ab cos C

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Magnitude of a real number
See Absolute value of a real number

nth power of a
The number with n factors of a , where n is the exponent and a is the base.

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Observational study
A process for gathering data from a subset of a population through current or past observations. This differs from an experiment in that no treatment is imposed.

Open interval
An interval that does not include its endpoints.

Opens upward or downward
A parabola y = ax 2 + bx + c opens upward if a > 0 and opens downward if a < 0.

Parallel lines
Two lines that are both vertical or have equal slopes.

Secant
The function y = sec x.

Symmetric about the yaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

System
A set of equations or inequalities.

Vertex form for a quadratic function
ƒ(x) = a(x  h)2 + k

Vertical stretch or shrink
See Stretch, Shrink.