 3.6.1: Find by implicit differentiation. (b) Solve the equation explicitly...
 3.6.2: Find by implicit differentiation. (b) Solve the equation explicitly...
 3.6.3: Find by implicit differentiation. (b) Solve the equation explicitly...
 3.6.4: Find by implicit differentiation. (b) Solve the equation explicitly...
 3.6.5: Find by implicit differentiation.
 3.6.6: Find by implicit differentiation.
 3.6.7: Find by implicit differentiation.
 3.6.8: Find by implicit differentiation.
 3.6.9: Find by implicit differentiation.
 3.6.10: Find by implicit differentiation.
 3.6.11: Find by implicit differentiation.
 3.6.12: Find by implicit differentiation.
 3.6.13: Find by implicit differentiation.
 3.6.14: Find by implicit differentiation.
 3.6.15: Find by implicit differentiation.
 3.6.16: Find by implicit differentiation.
 3.6.17: Find by implicit differentiation.
 3.6.18: Find by implicit differentiation.
 3.6.19: Find by implicit differentiation.
 3.6.20: Find by implicit differentiation.
 3.6.21: Regard as the independent variable and as the dependent variable an...
 3.6.22: Regard as the independent variable and as the dependent variable an...
 3.6.23: Regard as the independent variable and as the dependent variable an...
 3.6.24: Regard as the independent variable and as the dependent variable an...
 3.6.25: Use implicit differentiation to find an equation of the tangent lin...
 3.6.26: Use implicit differentiation to find an equation of the tangent lin...
 3.6.27: Use implicit differentiation to find an equation of the tangent lin...
 3.6.28: Use implicit differentiation to find an equation of the tangent lin...
 3.6.29: Use implicit differentiation to find an equation of the tangent lin...
 3.6.30: Use implicit differentiation to find an equation of the tangent lin...
 3.6.31: (a) The curve with equation is called a kampyle of Eudoxus. Find an...
 3.6.32: a) The curve with equation is called the Tschirnhausen cubic. Find ...
 3.6.33: Fanciful shapes can be created by using the implicit plotting capab...
 3.6.34: (a) The curve with equation has been likened to a bouncing wagon. U...
 3.6.35: Find the points on the lemniscate in Exercise 29 where the tangent ...
 3.6.36: Show by implicit differentiation that the tangent to the ellipse at...
 3.6.37: Find an equation of the tangent line to the hyperbola at the point .
 3.6.38: Show that the sum of the  and intercepts of any tangent line to t...
 3.6.39: Show, using implicit differentiation, that any tangent line at a po...
 3.6.40: The Power Rule can be proved using implicit differentiation for the...
 3.6.41: Find the derivative of the function. Simplify where possible.
 3.6.42: Find the derivative of the function. Simplify where possible.
 3.6.43: Find the derivative of the function. Simplify where possible.
 3.6.44: Find the derivative of the function. Simplify where possible.
 3.6.45: Find the derivative of the function. Simplify where possible.
 3.6.46: Find the derivative of the function. Simplify where possible.
 3.6.47: Find the derivative of the function. Simplify where possible.
 3.6.48: Find the derivative of the function. Simplify where possible.
 3.6.49: Find the derivative of the function. Simplify where possible.
 3.6.50: Find the derivative of the function. Simplify where possible.
 3.6.51: Find . Check that your answer is reasonable by comparing the graphs...
 3.6.52: Find . Check that your answer is reasonable by comparing the graphs...
 3.6.53: Prove the formula for by the same method as for .
 3.6.54: (a) One way of defining is to say that and or . Show that, with thi...
 3.6.55: Show that the given curves are orthogonal.
 3.6.56: Show that the given curves are orthogonal.
 3.6.57: Contour lines on a map of a hilly region are curves that join point...
 3.6.58: TV meteorologists often present maps showing pressure fronts. Such ...
 3.6.59: Show that the given families of curves are orthogonal trajectories ...
 3.6.60: Show that the given families of curves are orthogonal trajectories ...
 3.6.61: Show that the given families of curves are orthogonal trajectories ...
 3.6.62: Show that the given families of curves are orthogonal trajectories ...
 3.6.63: The equation represents a rotated ellipse, that is, an ellipse whos...
 3.6.64: (a) Where does the normal line to the ellipse at the point intersec...
 3.6.65: Find all points on the curve where the slope of the tangent line is .
 3.6.66: Find equations of both the tangent lines to the ellipse that pass t...
 3.6.67: (a) Suppose is a onetoone differentiable function and its inverse...
 3.6.68: (a) Show that is onetoone. (b) What is the value of ? (c) Use the...
 3.6.69: The figure shows a lamp located three units to the right of the ax...
Solutions for Chapter 3.6: Implicit Differentiation
Full solutions for Calculus,  5th Edition
ISBN: 9780534393397
Solutions for Chapter 3.6: Implicit Differentiation
Get Full SolutionsCalculus, was written by and is associated to the ISBN: 9780534393397. Chapter 3.6: Implicit Differentiation includes 69 full stepbystep solutions. This textbook survival guide was created for the textbook: Calculus,, edition: 5. Since 69 problems in chapter 3.6: Implicit Differentiation have been answered, more than 43738 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions.

Binomial
A polynomial with exactly two terms

Causation
A relationship between two variables in which the values of the response variable are directly affected by the values of the explanatory variable

Complex fraction
See Compound fraction.

Confounding variable
A third variable that affects either of two variables being studied, making inferences about causation unreliable

Cubic
A degree 3 polynomial function

Derivative of ƒ at x a
ƒ'(a) = lim x:a ƒ(x)  ƒ(a) x  a provided the limit exists

Difference identity
An identity involving a trigonometric function of u  v

Divergence
A sequence or series diverges if it does not converge

End behavior
The behavior of a graph of a function as.

Halfangle identity
Identity involving a trigonometric function of u/2.

Irrational zeros
Zeros of a function that are irrational numbers.

Multiplicity
The multiplicity of a zero c of a polynomial ƒ(x) of degree n > 0 is the number of times the factor (x  c) (x  z 2) Á (x  z n)

Parameter
See Parametric equations.

Quadrant
Any one of the four parts into which a plane is divided by the perpendicular coordinate axes.

Quotient polynomial
See Division algorithm for polynomials.

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

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

Semiminor axis
The distance from the center of an ellipse to a point on the ellipse along a line perpendicular to the major axis.

Symmetric property of equality
If a = b, then b = a

Transformation
A function that maps real numbers to real numbers.