 2.5.1: In Exercises 116, find by implicit differentiation. 10x21
 2.5.2: In Exercises 116, find by implicit differentiation. x21y
 2.5.3: In Exercises 116, find by implicit differentiation. 21y
 2.5.4: In Exercises 116, find by implicit differentiation. 1y1
 2.5.5: In Exercises 116, find by implicit differentiation. 1y1x
 2.5.6: In Exercises 116, find by implicit differentiation. y1xx
 2.5.7: In Exercises 116, find by implicit differentiation. 1xx
 2.5.8: In Exercises 116, find by implicit differentiation. 1xxy
 2.5.9: In Exercises 116, find by implicit differentiation. xxy2
 2.5.10: In Exercises 116, find by implicit differentiation. xy2
 2.5.11: In Exercises 116, find by implicit differentiation. y24
 2.5.12: In Exercises 116, find by implicit differentiation. y24x
 2.5.13: In Exercises 116, find by implicit differentiation. 24x
 2.5.14: In Exercises 116, find by implicit differentiation. 4xy
 2.5.15: In Exercises 116, find by implicit differentiation. 4xy3
 2.5.16: In Exercises 116, find by implicit differentiation. xy3y
 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: Famous Curves In Exercises 2932, find the slope of the tangent line...
 2.5.30: Famous Curves In Exercises 2932, find the slope of the tangent line...
 2.5.31: Famous Curves In Exercises 2932, find the slope of the tangent line...
 2.5.32: Famous Curves In Exercises 2932, find the slope of the tangent line...
 2.5.33: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.34: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.35: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.36: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.37: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.38: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.39: Famous Curves In Exercises 3340, find an equation of the tangent li...
 2.5.40: Famous Curves In Exercises 3340, find an equation of the tangent li...
 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 2y2
 2.5.46: In Exercises 4550, find in terms of and 2y2x
 2.5.47: In Exercises 4550, find in terms of and y2x2
 2.5.48: In Exercises 4550, find in terms of and 2x2
 2.5.49: In Exercises 4550, find in terms of and 2x2x
 2.5.50: In Exercises 4550, find in terms of and x2xy
 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: Orthogonal Trajectories In Exercises 5962, use a graphing utility t...
 2.5.60: Orthogonal Trajectories In Exercises 5962, use a graphing utility t...
 2.5.61: Orthogonal Trajectories In Exercises 5962, use a graphing utility t...
 2.5.62: Orthogonal Trajectories In Exercises 5962, use a graphing utility t...
 2.5.63: Orthogonal Trajectories In Exercises 63 and 64, verify that the two...
 2.5.64: Orthogonal Trajectories In Exercises 63 and 64, verify that the two...
 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: Orthogonal Trajectories The figure below shows the topographic map ...
 2.5.72: Weather Map The weather map shows several isobars curves that repre...
 2.5.73: Consider the equation (a) Use a graphing utility to graph the equat...
 2.5.74: Let be any tangent line to the curve Show that the sum of the and i...
 2.5.75: Prove (Theorem 2.3) that for the case in which is a rational number...
 2.5.76: Slope Find all points on the circle where the slope is 23x1
 2.5.77: Horizontal Tangent Determine the point(s) at which the graph of has...
 2.5.78: Tangent Lines Find equations of both tangent lines to the ellipse t...
 2.5.79: Normals to a Parabola The graph shows the normal lines from the poi...
 2.5.80: Normal Lines (a) Find an equation of the normal line to the ellipse...
Solutions for Chapter 2.5: Implicit Differentiation
Full solutions for Calculus  8th Edition
ISBN: 9780618502981
Solutions for Chapter 2.5: Implicit Differentiation
Get Full SolutionsCalculus was written by and is associated to the ISBN: 9780618502981. This textbook survival guide was created for the textbook: Calculus, edition: 8. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2.5: Implicit Differentiation includes 80 full stepbystep solutions. Since 80 problems in chapter 2.5: Implicit Differentiation have been answered, more than 83850 students have viewed full stepbystep solutions from this chapter.

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Cubic
A degree 3 polynomial function

Dot product
The number found when the corresponding components of two vectors are multiplied and then summed

Index
See Radical.

Instantaneous velocity
The instantaneous rate of change of a position function with respect to time, p. 737.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Linear combination of vectors u and v
An expression au + bv , where a and b are real numbers

Matrix, m x n
A rectangular array of m rows and n columns of real numbers

Median (of a data set)
The middle number (or the mean of the two middle numbers) if the data are listed in order.

Normal distribution
A distribution of data shaped like the normal curve.

Positive linear correlation
See Linear correlation.

Reciprocal identity
An identity that equates a trigonometric function with the reciprocal of another trigonometricfunction.

Removable discontinuity at x = a
lim x:a ƒ(x) = limx:a+ ƒ(x) but either the common limit is not equal ƒ(a) to ƒ(a) or is not defined

Row echelon form
A matrix in which rows consisting of all 0’s occur only at the bottom of the matrix, the first nonzero entry in any row with nonzero entries is 1, and the leading 1’s move to the right as we move down the rows.

Scientific notation
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Standard position (angle)
An angle positioned on a rectangular coordinate system with its vertex at the origin and its initial side on the positive xaxis

Trigonometric form of a complex number
r(cos ? + i sin ?)

Vector
An ordered pair <a, b> of real numbers in the plane, or an ordered triple <a, b, c> of real numbers in space. A vector has both magnitude and direction.

Vertical asymptote
The line x = a is a vertical asymptote of the graph of the function ƒ if limx:a+ ƒ1x2 = q or lim x:a ƒ1x2 = q.