 2.5.1: In Exercises 116, find by implicit differentiation.
 2.5.2: In Exercises 116, find by implicit differentiation.
 2.5.3: In Exercises 116, find by implicit differentiation.
 2.5.4: In Exercises 116, find by implicit differentiation.
 2.5.5: In Exercises 116, find by implicit differentiation.
 2.5.6: In Exercises 116, find by implicit differentiation.x 2y y 2 x x 2 3
 2.5.7: In Exercises 116, find by implicit differentiation
 2.5.8: In Exercises 116, find by implicit differentiationxy x2 x y 1 3
 2.5.9: In Exercises 116, find by implicit differentiation
 2.5.10: In Exercises 116, find by implicit differentiation4 cos x sin y 1 3
 2.5.11: In Exercises 116, find by implicit differentiation
 2.5.12: In Exercises 116, find by implicit differentiation
 2.5.13: In Exercises 116, find by implicit differentiationsin x x1 tan y c
 2.5.14: In Exercises 116, find by implicit differentiationcot y x y s
 2.5.15: In Exercises 116, find by implicit differentiation.y sin xy
 2.5.16: In Exercises 116, find by implicit differentiation.x sec 1 y
 2.5.17: In Exercises 1720, (a) find two explicit functions by solving the e...
 2.5.18: In Exercises 1720, (a) find two explicit functions by solving the e...
 2.5.19: In Exercises 1720, (a) find two explicit functions by solving the e...
 2.5.20: In Exercises 1720, (a) find two explicit functions by solving the e...
 2.5.21: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.22: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.23: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.24: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.25: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.26: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.27: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.28: In Exercises 2128, find by implicit differentiation and evaluate th...
 2.5.29: In Exercises 29 32, find the slope of the tangent line to the graph...
 2.5.30: In Exercises 29 32, find the slope of the tangent line to the graph...
 2.5.31: In Exercises 29 32, find the slope of the tangent line to the graph...
 2.5.32: In Exercises 29 32, find the slope of the tangent line to the graph...
 2.5.33: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.34: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.35: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.36: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.37: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.38: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.39: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.40: In Exercises 33 40, find an equation of the tangent line to the gra...
 2.5.41: (a) Use implicit differentiation to find an equation of the tangent...
 2.5.42: (a) Use implicit differentiation to find an equation of the tangent...
 2.5.43: In Exercises 43 and 44, find implicitly and find the largest interv...
 2.5.44: In Exercises 43 and 44, find implicitly and find the largest interv...
 2.5.45: In Exercises 4550, find in terms of and
 2.5.46: In Exercises 4550, find in terms of and
 2.5.47: In Exercises 4550, find in terms of and
 2.5.48: In Exercises 4550, find in terms of and
 2.5.49: In Exercises 4550, find in terms of and
 2.5.50: In Exercises 4550, find in terms of and
 2.5.51: In Exercises 51 and 52, use a graphing utility to graph the equatio...
 2.5.52: In Exercises 51 and 52, use a graphing utility to graph the equatio...
 2.5.53: In Exercises 53 and 54, find equations for the tangent line and nor...
 2.5.54: In Exercises 53 and 54, find equations for the tangent line and nor...
 2.5.55: Show that the normal line at any point on the circle passes through...
 2.5.56: Two circles of radius 4 are tangent to the graph of at the point Fi...
 2.5.57: In Exercises 57 and 58, find the points at which the graph of the e...
 2.5.58: In Exercises 57 and 58, find the points at which the graph of the e...
 2.5.59: In Exercises 59 62, use a graphing utility to sketch the intersecti...
 2.5.60: In Exercises 59 62, use a graphing utility to sketch the intersecti...
 2.5.61: In Exercises 59 62, use a graphing utility to sketch the intersecti...
 2.5.62: In Exercises 59 62, use a graphing utility to sketch the intersecti...
 2.5.63: In Exercises 63 and 64, verify that the two families of curves are ...
 2.5.64: In Exercises 63 and 64, verify that the two families of curves are ...
 2.5.65: In Exercises 6568, differentiate (a) with respect to ( is a functio...
 2.5.66: In Exercises 6568, differentiate (a) with respect to ( is a functio...
 2.5.67: In Exercises 6568, differentiate (a) with respect to ( is a functio...
 2.5.68: In Exercises 6568, differentiate (a) with respect to ( is a functio...
 2.5.69: Describe the difference between the explicit form of a function and...
 2.5.70: Describe the difference between the explicit form of a function and...
 2.5.71: The figure below shows the topographic map carried by a group of hi...
 2.5.72: The weather map shows several isobars curves that represent areas o...
 2.5.73: Consider the equation (a) Use a graphing utility to graph the equat...
 2.5.74: Determine if the statement is true. If it is false, explain why and...
 2.5.75: Let be any tangent line to the curve Show that the sum of the and i...
 2.5.76: Prove (Theorem 2.3) that for the case in which is a rational number...
 2.5.77: Find all points on the circle where the slope is 3/4
 2.5.78: Determine the point(s) at which the graph of has a horizontal tangent.
 2.5.79: Find equations of both tangent lines to the ellipse that passes thr...
 2.5.80: The graph shows the normal lines from the point to the graph of the...
 2.5.81: (a) Find an equation of the normal line to the ellipse at the point...
Solutions for Chapter 2.5: Implicit Differentiation
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 2.5: Implicit Differentiation
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780547167022. Chapter 2.5: Implicit Differentiation includes 81 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus , edition: 9. Since 81 problems in chapter 2.5: Implicit Differentiation have been answered, more than 64068 students have viewed full stepbystep solutions from this chapter.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Additive inverse of a real number
The opposite of b , or b

Central angle
An angle whose vertex is the center of a circle

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Difference identity
An identity involving a trigonometric function of u  v

Doubleblind experiment
A blind experiment in which the researcher gathering data from the subjects is not told which subjects have received which treatment

First quartile
See Quartile.

Geometric series
A series whose terms form a geometric sequence.

Imaginary unit
The complex number.

Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.

Range (in statistics)
The difference between the greatest and least values in a data set.

Real axis
See Complex plane.

Recursively defined sequence
A sequence defined by giving the first term (or the first few terms) along with a procedure for finding the subsequent terms.

Replication
The principle of experimental design that minimizes the effects of chance variation by repeating the experiment multiple times.

Sum of complex numbers
(a + bi) + (c + di) = (a + c) + (b + d)i

Variable
A letter that represents an unspecified number.

Vertex of a cone
See Right circular cone.

Vertical line
x = a.

Zero of a function
A value in the domain of a function that makes the function value zero.

Zero vector
The vector <0,0> or <0,0,0>.