 4.4.1: In 128, differentiate the functions with respect to the independent...
 4.4.2: In 128, differentiate the functions with respect to the independent...
 4.4.3: In 128, differentiate the functions with respect to the independent...
 4.4.4: In 128, differentiate the functions with respect to the independent...
 4.4.5: In 128, differentiate the functions with respect to the independent...
 4.4.6: In 128, differentiate the functions with respect to the independent...
 4.4.7: In 128, differentiate the functions with respect to the independent...
 4.4.8: In 128, differentiate the functions with respect to the independent...
 4.4.9: In 128, differentiate the functions with respect to the independent...
 4.4.10: In 128, differentiate the functions with respect to the independent...
 4.4.11: In 128, differentiate the functions with respect to the independent...
 4.4.12: In 128, differentiate the functions with respect to the independent...
 4.4.13: In 128, differentiate the functions with respect to the independent...
 4.4.14: In 128, differentiate the functions with respect to the independent...
 4.4.15: In 128, differentiate the functions with respect to the independent...
 4.4.16: In 128, differentiate the functions with respect to the independent...
 4.4.17: In 128, differentiate the functions with respect to the independent...
 4.4.18: In 128, differentiate the functions with respect to the independent...
 4.4.19: In 128, differentiate the functions with respect to the independent...
 4.4.20: In 128, differentiate the functions with respect to the independent...
 4.4.21: In 128, differentiate the functions with respect to the independent...
 4.4.22: In 128, differentiate the functions with respect to the independent...
 4.4.23: In 128, differentiate the functions with respect to the independent...
 4.4.24: In 128, differentiate the functions with respect to the independent...
 4.4.25: In 128, differentiate the functions with respect to the independent...
 4.4.26: In 128, differentiate the functions with respect to the independent...
 4.4.27: In 128, differentiate the functions with respect to the independent...
 4.4.28: In 128, differentiate the functions with respect to the independent...
 4.4.29: Differentiate f (x) = (ax + 1)3 with respect to x. Assume that a is...
 4.4.30: Differentiate f (x) = _ ax2 2 with respect to x. Assume that a is a...
 4.4.31: Differentiate g(N) = bN (k + N)2 with respect to N. Assume that b a...
 4.4.32: Differentiate g(N) = N (k + bN)3 with respect to N. Assume that b a...
 4.4.33: Differentiate g(T ) = a(T0 T )3 b with respect to T . Assume that a...
 4.4.34: Suppose that f _ (x) = 2x + 1. Find the following: (a) d dx f (x2) ...
 4.4.35: Suppose that f _ (x) = 1 x . Find the following: (a) d dx f (x2 + 3...
 4.4.36: In 3639, assume that f (x) and g(x) are differentiable. Find d dx f...
 4.4.37: In 3639, assume that f (x) and g(x) are differentiable. Find d dx _...
 4.4.38: In 3639, assume that f (x) and g(x) are differentiable. Find d dx f...
 4.4.39: In 3639, assume that f (x) and g(x) are differentiable. Find d dx [...
 4.4.40: In 4046, find dy dx by applying the chain rule repeatedly y = ( _ 1...
 4.4.41: In 4046, find dy dx by applying the chain rule repeatedly y = ( _ x...
 4.4.42: In 4046, find dy dx by applying the chain rule repeatedly y = 1 + 2...
 4.4.43: In 4046, find dy dx by applying the chain rule repeatedly y = 1 + (...
 4.4.44: In 4046, find dy dx by applying the chain rule repeatedly y = _ x 2...
 4.4.45: In 4046, find dy dx by applying the chain rule repeatedly y = _ 2x ...
 4.4.46: In 4046, find dy dx by applying the chain rule repeatedly y = _ (2x...
 4.4.47: In 4754, find dy dx by implicit differentiation x2 + y2 = 4
 4.4.48: In 4754, find dy dx by implicit differentiation y = x2 + 3yx
 4.4.49: In 4754, find dy dx by implicit differentiation x3/4 + y3/4 = 1
 4.4.50: In 4754, find dy dx by implicit differentiation xy y3 = 1
 4.4.51: In 4754, find dy dx by implicit differentiation xy = x2 + 1
 4.4.52: In 4754, find dy dx by implicit differentiation 1 2xy y3 = 4
 4.4.53: In 4754, find dy dx by implicit differentiation x y = y x
 4.4.54: In 4754, find dy dx by implicit differentiation x xy + 1 = 2xy
 4.4.55: In 5557, find the lines that are (a) tangential and (b) normal to e...
 4.4.56: In 5557, find the lines that are (a) tangential and (b) normal to e...
 4.4.57: In 5557, find the lines that are (a) tangential and (b) normal to e...
 4.4.58: Lemniscate (a) The curve with equation y2 = x2 x4 is shaped like th...
 4.4.59: Astroid (a) Consider the curve with equation x2/3 + y2/3 = 4. Find ...
 4.4.60: Kampyle of Eudoxus (a) Consider the curve with equation y2 = 10x4 x...
 4.4.61: Assume that x and y are differentiable functions of t. Find dy dt w...
 4.4.62: Assume that x and y are differentiable functions of t. Find dy dt w...
 4.4.63: Assume that x and y are differentiable functions of t. Find dy dt w...
 4.4.64: Assume that u and v are differentiable functions of t. Find du dt w...
 4.4.65: Assume that the side length x and the volume V = x3 of a cube are d...
 4.4.66: Assume that the radius r and the area A = r 2 of a circle are diffe...
 4.4.67: Assume that the radius r and the surface area S = 4r 2 of a sphere ...
 4.4.68: Assume that the radius r and the volume V = 4 3r 3 of a sphere are ...
 4.4.69: Suppose that water is stored in a cylindrical tank of radius 5 m. I...
 4.4.70: Suppose that we pump water into an inverted right circular conical ...
 4.4.71: Two people start biking from the same point. One bikes east at 15 m...
 4.4.72: Allometric equations describe the scaling relationship between two ...
 4.4.73: In 7382, find the first and the second derivatives of each function...
 4.4.74: In 7382, find the first and the second derivatives of each function...
 4.4.75: In 7382, find the first and the second derivatives of each function...
 4.4.76: In 7382, find the first and the second derivatives of each function...
 4.4.77: In 7382, find the first and the second derivatives of each function...
 4.4.78: In 7382, find the first and the second derivatives of each function...
 4.4.79: In 7382, find the first and the second derivatives of each function...
 4.4.80: In 7382, find the first and the second derivatives of each function...
 4.4.81: In 7382, find the first and the second derivatives of each function...
 4.4.82: In 7382, find the first and the second derivatives of each function...
 4.4.83: Find the first 10 derivatives of y = x5.
 4.4.84: Find f (n)(x) and f (n+1)(x) of f (x) = xn.
 4.4.85: Find a seconddegree polynomial p(x) = ax2 + bx + c with p(0) = 3, ...
 4.4.86: The position at time t of a particle that moves along a straight li...
 4.4.87: Neglecting air resistance, the height h (in meters) of an object th...
Solutions for Chapter 4.4: The Chain Rule and Higher Derivatives
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 4.4: The Chain Rule and Higher Derivatives
Get Full SolutionsSince 87 problems in chapter 4.4: The Chain Rule and Higher Derivatives have been answered, more than 20212 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Calculus For Biology and Medicine (Calculus for Life Sciences Series), edition: 3. Chapter 4.4: The Chain Rule and Higher Derivatives includes 87 full stepbystep solutions. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688. This expansive textbook survival guide covers the following chapters and their solutions.

Compounded monthly
See Compounded k times per year.

Correlation coefficient
A measure of the strength of the linear relationship between two variables, pp. 146, 162.

Cosecant
The function y = csc x

Cycloid
The graph of the parametric equations

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

Finite sequence
A function whose domain is the first n positive integers for some fixed integer n.

Focal width of a parabola
The length of the chord through the focus and perpendicular to the axis.

Inequality symbol or
<,>,<,>.

Nautical mile
Length of 1 minute of arc along the Earth’s equator.

Number line graph of a linear inequality
The graph of the solutions of a linear inequality (in x) on a number line

Order of magnitude (of n)
log n.

Paraboloid of revolution
A surface generated by rotating a parabola about its line of symmetry.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Principle of mathematical induction
A principle related to mathematical induction.

Product of matrices A and B
The matrix in which each entry is obtained by multiplying the entries of a row of A by the corresponding entries of a column of B and then adding

Quadratic formula
The formula x = b 2b2  4ac2a used to solve ax 2 + bx + c = 0.

Radian measure
The measure of an angle in radians, or, for a central angle, the ratio of the length of the intercepted arc tothe radius of the circle.

Regression model
An equation found by regression and which can be used to predict unknown values.

Square matrix
A matrix whose number of rows equals the number of columns.

Triangular number
A number that is a sum of the arithmetic series 1 + 2 + 3 + ... + n for some natural number n.