 4.3.1: In 116, use the product rule to find the derivative with respect to...
 4.3.2: In 116, use the product rule to find the derivative with respect to...
 4.3.3: In 116, use the product rule to find the derivative with respect to...
 4.3.4: In 116, use the product rule to find the derivative with respect to...
 4.3.5: In 116, use the product rule to find the derivative with respect to...
 4.3.6: In 116, use the product rule to find the derivative with respect to...
 4.3.7: In 116, use the product rule to find the derivative with respect to...
 4.3.8: In 116, use the product rule to find the derivative with respect to...
 4.3.9: In 116, use the product rule to find the derivative with respect to...
 4.3.10: In 116, use the product rule to find the derivative with respect to...
 4.3.11: In 116, use the product rule to find the derivative with respect to...
 4.3.12: In 116, use the product rule to find the derivative with respect to...
 4.3.13: In 116, use the product rule to find the derivative with respect to...
 4.3.14: In 116, use the product rule to find the derivative with respect to...
 4.3.15: In 116, use the product rule to find the derivative with respect to...
 4.3.16: In 116, use the product rule to find the derivative with respect to...
 4.3.17: In 1720, apply the product rule to find the tangent line, in slopei...
 4.3.18: In 1720, apply the product rule to find the tangent line, in slopei...
 4.3.19: In 1720, apply the product rule to find the tangent line, in slopei...
 4.3.20: In 1720, apply the product rule to find the tangent line, in slopei...
 4.3.21: In 2124, apply the product rule to find the normal line, in slopein...
 4.3.22: In 2124, apply the product rule to find the normal line, in slopein...
 4.3.23: In 2124, apply the product rule to find the normal line, in slopein...
 4.3.24: In 2124, apply the product rule to find the normal line, in slopein...
 4.3.25: In 2528, apply the product rule repeatedly to find the derivative o...
 4.3.26: In 2528, apply the product rule repeatedly to find the derivative o...
 4.3.27: In 2528, apply the product rule repeatedly to find the derivative o...
 4.3.28: In 2528, apply the product rule repeatedly to find the derivative o...
 4.3.29: Differentiate f (x) = a(x 1)(2x 1) with respect to x. Assume that a...
 4.3.30: Differentiate f (x) = (a x)(a + x) with respect to x. Assume that a...
 4.3.31: Differentiate f (x) = 2a(x2 a)2 + a with respect to x. Assume that ...
 4.3.32: Differentiate f (x) = 3(x 1)2 2 + a with respect to x. Assume that ...
 4.3.33: Differentiate g(t) = (at + 1)2 with respect to t. Assume that a is ...
 4.3.34: Differentiate h(t) = a(t a) + a with respect to t. Assume that a is...
 4.3.35: Suppose that f (2) = 4, g(2) = 3, f _ (2) = 1, and g_ (2) = 2. Find...
 4.3.36: Suppose that f (2) = 4, g(2) = 3, f _ (2) = 1, and g_ (2) = 2. Find...
 4.3.37: In 3740, assume that f (x) is differentiable. Find an expression fo...
 4.3.38: In 3740, assume that f (x) is differentiable. Find an expression fo...
 4.3.39: In 3740, assume that f (x) is differentiable. Find an expression fo...
 4.3.40: In 3740, assume that f (x) is differentiable. Find an expression fo...
 4.3.41: In 4144, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.42: In 4144, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.43: In 4144, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.44: In 4144, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.45: Let B(t) denote the biomass at time t with specific growth rate g(B...
 4.3.46: Let N(t) denote the size of a population at time t. Differentiate f...
 4.3.47: Let N(t) denote the size of a population at time t. Differentiate f...
 4.3.48: Consider the chemical reaction A + B AB If x denotes the concentrat...
 4.3.49: In 4970, differentiate with respect to the independent variable. f ...
 4.3.50: In 4970, differentiate with respect to the independent variable. f ...
 4.3.51: In 4970, differentiate with respect to the independent variable. f ...
 4.3.52: In 4970, differentiate with respect to the independent variable. f ...
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 4.3.54: In 4970, differentiate with respect to the independent variable. f ...
 4.3.55: In 4970, differentiate with respect to the independent variable. h(...
 4.3.56: In 4970, differentiate with respect to the independent variable. h(...
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 4.3.58: In 4970, differentiate with respect to the independent variable. f ...
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 4.3.69: In 4970, differentiate with respect to the independent variable. f ...
 4.3.70: In 4970, differentiate with respect to the independent variable. f ...
 4.3.71: In 7174, find the tangent line, in slopeintercept form, of y = f (x...
 4.3.72: In 7174, find the tangent line, in slopeintercept form, of y = f (x...
 4.3.73: In 7174, find the tangent line, in slopeintercept form, of y = f (x...
 4.3.74: In 7174, find the tangent line, in slopeintercept form, of y = f (x...
 4.3.75: Differentiate f (x) = ax 3 + x with respect to x. Assume that a is ...
 4.3.76: Differentiate f (x) = ax k + x with respect to x. Assume that a and...
 4.3.77: Differentiate f (x) = ax2 4 + x2 with respect to x. Assume that a i...
 4.3.78: Differentiate f (x) = ax2 k2 + x2 with respect to x. Assume that a ...
 4.3.79: Differentiate f (R) = Rn kn + Rn with respect to R. Assume that k i...
 4.3.80: Differentiate h(t) = at(1 a) + a with respect to t. Assume that a i...
 4.3.81: Differentiate h(t) = at(t a) + at with respect to t. Assume that a ...
 4.3.82: Suppose that f (2) = 4, g(2) = 3, f _ (2) = 1, and g_ (2) = 2. Find...
 4.3.83: Suppose that f (2) = 4, g(2) = 3, f _ (2) = 1, and g_ (2) = 2. Find...
 4.3.84: In 8487, assume that f (x) is differentiable. Find an expression fo...
 4.3.85: In 8487, assume that f (x) is differentiable. Find an expression fo...
 4.3.86: In 8487, assume that f (x) is differentiable. Find an expression fo...
 4.3.87: In 8487, assume that f (x) is differentiable. Find an expression fo...
 4.3.88: In 8891, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.89: In 8891, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.90: In 8891, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.91: In 8891, assume that f (x) and g(x) are differentiable at x. Find a...
 4.3.92: Assume that f (x) is a differentiable function. Find the derivative...
 4.3.93: Find the tangent line to the hyperbola yx = c, where c is a positiv...
 4.3.94: The males in the frog species (found in Puerto Rico) take care of t...
Solutions for Chapter 4.3: The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 4.3: The Product and Quotient Rules, and the Derivatives of Rational and Power Functions
Get Full SolutionsChapter 4.3: The Product and Quotient Rules, and the Derivatives of Rational and Power Functions includes 94 full stepbystep solutions. Since 94 problems in chapter 4.3: The Product and Quotient Rules, and the Derivatives of Rational and Power Functions have been answered, more than 21733 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. This expansive textbook survival guide covers the following chapters and their solutions. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by and is associated to the ISBN: 9780321644688.

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

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

Combination
An arrangement of elements of a set, in which order is not important

Common ratio
See Geometric sequence.

Complex conjugates
Complex numbers a + bi and a  bi

Compounded k times per year
Interest compounded using the formula A = Pa1 + rkbkt where k = 1 is compounded annually, k = 4 is compounded quarterly k = 12 is compounded monthly, etc.

Coterminal angles
Two angles having the same initial side and the same terminal side

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

DMS measure
The measure of an angle in degrees, minutes, and seconds

Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.

Law of sines
sin A a = sin B b = sin C c

Linear system
A system of linear equations

Lower bound test for real zeros
A test for finding a lower bound for the real zeros of a polynomial

Parameter
See Parametric equations.

Product of a scalar and a vector
The product of scalar k and vector u = 8u1, u29 1or u = 8u1, u2, u392 is k.u = 8ku1, ku291or k # u = 8ku1, ku2, ku392,

Quadratic function
A function that can be written in the form ƒ(x) = ax 2 + bx + c, where a, b, and c are real numbers, and a ? 0.

Reflection across the yaxis
x, y and (x,y) are reflections of each other across the yaxis.

Remainder theorem
If a polynomial f(x) is divided by x  c , the remainder is ƒ(c)

Series
A finite or infinite sum of terms.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically