 10.5.1: Let f (x, y) = x2 + y2 with x(t) = 3t and y(t) = et . Find the deri...
 10.5.2: Let f (x, y) = ex sin y with x(t) = t and y(t) = t3. Find the deriv...
 10.5.3: Let f (x, y) = _ x2 + y2 with x(t) = t and y(t) = sin t. Find the d...
 10.5.4: Let f (x, y) = ln(xy x2) with x(t) = t2 and y(t) = t. Find the deri...
 10.5.5: Let f (x, y) = 1 x + 1 y with x(t) = sin t and y(t) = cos t. Find t...
 10.5.6: Let f (x, y) = xey with x(t) = et and y(t) = t2. Find the derivativ...
 10.5.7: Find dz dt for z = f (x, y) with x = u(t) and y = v(t).
 10.5.8: Find dw dt for w = e f (x,y) with x = u(t) and y = v(t).
 10.5.9: Find dy dx if (x2 + y2)ey = 0.
 10.5.10: Find dy dx if (sin x + cos y)x2 = 0.
 10.5.11: Find dy dx if ln(x2 + y2) = 3xy.
 10.5.12: Find dy dx if cos(x2 + y2) = sin(x2 y2).
 10.5.13: Find dy dx if y = arccos x.
 10.5.14: Find dy dx if y = arctan x.
 10.5.15: The growth rate r of a particular organism is affected by both the ...
 10.5.16: Suppose that you travel along an environmental gradient, along whic...
 10.5.17: In 1724, find the gradient of each function. f (x, y) = x3 y2
 10.5.18: In 1724, find the gradient of each function. f (x, y) = xy x2+y2
 10.5.19: In 1724, find the gradient of each function. f (x, y) = _ x3 3xy
 10.5.20: In 1724, find the gradient of each function. f (x, y) = x(x2 y2)2/3
 10.5.21: In 1724, find the gradient of each function. f (x, y) = exp __ x2 +...
 10.5.22: In 1724, find the gradient of each function. f (x, y) = tan xy x+y
 10.5.23: In 1724, find the gradient of each function. f (x, y) = ln _ x y + ...
 10.5.24: In 1724, find the gradient of each function. f (x, y) = cos(3x2 2y2...
 10.5.25: In 2530, compute the directional derivative of f (x, y) at the give...
 10.5.26: In 2530, compute the directional derivative of f (x, y) at the give...
 10.5.27: In 2530, compute the directional derivative of f (x, y) at the give...
 10.5.28: In 2530, compute the directional derivative of f (x, y) at the give...
 10.5.29: In 2530, compute the directional derivative of f (x, y) at the give...
 10.5.30: In 2530, compute the directional derivative of f (x, y) at the give...
 10.5.31: In 3134, compute the directional derivative of f (x, y) at the poin...
 10.5.32: In 3134, compute the directional derivative of f (x, y) at the poin...
 10.5.33: In 3134, compute the directional derivative of f (x, y) at the poin...
 10.5.34: In 3134, compute the directional derivative of f (x, y) at the poin...
 10.5.35: In what direction does f (x, y) = 3xy x2 increase most rapidly at (...
 10.5.36: In what direction does f (x, y) = ex cos y increase most rapidly at...
 10.5.37: In what direction does f (x, y) = _ x2 y2 increase most rapidly at ...
 10.5.38: In what direction does f (x, y) = ln(x2 + y2) increase most rapidly...
 10.5.39: Find a unit vector that is normal to the level curve of the functio...
 10.5.40: Find a unit vector that is normal to the level curve of the functio...
 10.5.41: Find a unit vector that is normal to the level curve of the functio...
 10.5.42: Find a unit vector that is normal to the level curve of the functio...
 10.5.43: Chemotaxis Chemotaxis is the chemically directed movement of organi...
 10.5.44: Suppose an organism moves down a sloped surface along the steepest ...
Solutions for Chapter 10.5: More about Derivatives (Optional)
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 10.5: More about Derivatives (Optional)
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus For Biology and Medicine (Calculus for Life Sciences Series), edition: 3. Chapter 10.5: More about Derivatives (Optional) includes 44 full stepbystep solutions. Since 44 problems in chapter 10.5: More about Derivatives (Optional) have been answered, more than 20308 students have viewed full stepbystep solutions from this chapter. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688.

Common difference
See Arithmetic sequence.

Directed line segment
See Arrow.

Divergence
A sequence or series diverges if it does not converge

Future value of an annuity
The net amount of money returned from an annuity.

Independent events
Events A and B such that P(A and B) = P(A)P(B)

Index
See Radical.

Linear factorization theorem
A polynomial ƒ(x) of degree n > 0 has the factorization ƒ(x) = a(x1  z1) 1x  i z 22 Á 1x  z n where the z1 are the zeros of ƒ

Ordered set
A set is ordered if it is possible to compare any two elements and say that one element is “less than” or “greater than” the other.

Placebo
In an experimental study, an inactive treatment that is equivalent to the active treatment in every respect except for the factor about which an inference is to be made. Subjects in a blind experiment do not know if they have been given the active treatment or the placebo.

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Positive angle
Angle generated by a counterclockwise rotation.

Principle of mathematical induction
A principle related to mathematical induction.

Range of a function
The set of all output values corresponding to elements in the domain.

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Rational zeros theorem
A procedure for finding the possible rational zeros of a polynomial.

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

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Slope
Ratio change in y/change in x

Standard deviation
A measure of how a data set is spread

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.