- 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
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
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
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.
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.
Two lines that are both vertical or have equal slopes.
The function y = sec x.
Symmetric about the y-axis
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
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.