 4.2.1: Differentiate the functions given in 122 with respect to the indepe...
 4.2.2: Differentiate the functions given in 122 with respect to the indepe...
 4.2.3: Differentiate the functions given in 122 with respect to the indepe...
 4.2.4: Differentiate the functions given in 122 with respect to the indepe...
 4.2.5: Differentiate the functions given in 122 with respect to the indepe...
 4.2.6: Differentiate the functions given in 122 with respect to the indepe...
 4.2.7: Differentiate the functions given in 122 with respect to the indepe...
 4.2.8: Differentiate the functions given in 122 with respect to the indepe...
 4.2.9: Differentiate the functions given in 122 with respect to the indepe...
 4.2.10: Differentiate the functions given in 122 with respect to the indepe...
 4.2.11: Differentiate the functions given in 122 with respect to the indepe...
 4.2.12: Differentiate the functions given in 122 with respect to the indepe...
 4.2.13: Differentiate the functions given in 122 with respect to the indepe...
 4.2.14: Differentiate the functions given in 122 with respect to the indepe...
 4.2.15: Differentiate the functions given in 122 with respect to the indepe...
 4.2.16: Differentiate the functions given in 122 with respect to the indepe...
 4.2.17: Differentiate the functions given in 122 with respect to the indepe...
 4.2.18: Differentiate the functions given in 122 with respect to the indepe...
 4.2.19: Differentiate the functions given in 122 with respect to the indepe...
 4.2.20: Differentiate the functions given in 122 with respect to the indepe...
 4.2.21: Differentiate the functions given in 122 with respect to the indepe...
 4.2.22: Differentiate the functions given in 122 with respect to the indepe...
 4.2.23: Differentiate f (x) = ax3 with respect to x. Assume that a is a con...
 4.2.24: Differentiate f (x) = x3 + a with respect to x. Assume that a is a ...
 4.2.25: Differentiate f (x) = ax2 2a with respect to x. Assume that a is a ...
 4.2.26: Differentiate f (x) = a2x4 2ax2 with respect to x. Assume that a is...
 4.2.27: Differentiate h(s) = rs2 r with respect to s. Assume that r is a co...
 4.2.28: Differentiate f (r ) = rs2 r with respect to r . Assume that s is a...
 4.2.29: Differentiate f (x) = rs2x3 rx + s with respect to x. Assume that r...
 4.2.30: Differentiate f (x) = r + x rs2 rsx + (r + s)x rs with respect to x...
 4.2.31: Differentiate f (N) = (b 1)N4 N2 b with respect to N. Assume that b...
 4.2.32: Differentiate f (N) = bN2 + N K + b with respect to N. Assume that ...
 4.2.33: Differentiate g(t) = a3t at3 with respect to t. Assume that a is a ...
 4.2.34: Differentiate h(s) = a4s2 as4 + s2 a4 with respect to s. Assume tha...
 4.2.35: Differentiate V(t) = V0(1 + t) with respect to t. Assume that V0 an...
 4.2.36: Differentiate p(T ) = NkT V with respect to T . Assume that N, k, a...
 4.2.37: Differentiate g(N) = N _ 1 N K _ with respect to N. Assume that K i...
 4.2.38: Differentiate g(N) = rN _ 1 N K _ with respect to N. Assume that K ...
 4.2.39: Differentiate g(N) = rN2 _ 1 N K _ with respect to N. Assume that K...
 4.2.40: Differentiate g(N) = rN (a N) _ 1 N K _ with respect to N. Assume t...
 4.2.41: Differentiate R(T ) = 25 15 k4 c2h3 T 4 with respect to T . Assume ...
 4.2.42: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.43: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.44: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.45: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.46: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.47: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.48: In 4248, find the tangent line, in standard form, to y = f (x) at t...
 4.2.49: In 4954, find the normal line, in standard form, to y = f (x) at th...
 4.2.50: In 4954, find the normal line, in standard form, to y = f (x) at th...
 4.2.51: In 4954, find the normal line, in standard form, to y = f (x) at th...
 4.2.52: In 4954, find the normal line, in standard form, to y = f (x) at th...
 4.2.53: In 4954, find the normal line, in standard form, to y = f (x) at th...
 4.2.54: In 4954, find the normal line, in standard form, to y = f (x) at th...
 4.2.55: Find the tangent line to f (x) = ax2 at x = 1. Assume that a is a p...
 4.2.56: Find the tangent line to f (x) = ax3 2ax at x = 1. Assume that a is...
 4.2.57: Find the tangent line to f (x) = ax2 a2 + 2 at x = 2. Assume that a...
 4.2.58: Find the tangent line to f (x) = x2 a + 1 at x = a. Assume that a i...
 4.2.59: Find the normal line to f (x) = ax3 at x = 1. Assume that a is a po...
 4.2.60: Find the normal line to f (x) = ax2 3ax at x = 2. Assume that a is ...
 4.2.61: Find the normal line to f (x) = ax2 a + 1 at x = 2. Assume that a i...
 4.2.62: Find the normal line to f (x) = x3 a + 1 at x = 2a. Assume that a i...
 4.2.63: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.64: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.65: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.66: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.67: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.68: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.69: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.70: In 6370, find the coordinates of all of the points of the graph of ...
 4.2.71: Find a point on the curve y = 4 x2 whose tangent line is parallel t...
 4.2.72: Find a point on the curve y = (4 x)2 whose tangent line is parallel...
 4.2.73: Find a point on the curve y = 2x2 1 2 whose tangent line is paralle...
 4.2.74: Find a point on the curve y = 1 3x3 whose tangent line is parallel ...
 4.2.75: Find a point on the curve y = x3 + 2x + 2 whose tangent line is par...
 4.2.76: Find a point on the curve y = 2x3 4x + 1 whose tangent line is para...
 4.2.77: Show that the tangent line to the curve y = x2 at the point (1, 1) ...
 4.2.78: Find all tangent lines to the curve y = x2 that pass through the po...
 4.2.79: Find all tangent lines to the curve y = x2 that pass through the po...
 4.2.80: How many tangent lines to the curve y = x2 + 2x pass through the po...
 4.2.81: Suppose that P(x) is a polynomial of degree 4. Is P_ (x) a polynomi...
 4.2.82: Suppose that P(x) is a polynomial of degree k. Is P_ (x) a polynomi...
Solutions for Chapter 4.2: The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials
Full solutions for Calculus For Biology and Medicine (Calculus for Life Sciences Series)  3rd Edition
ISBN: 9780321644688
Solutions for Chapter 4.2: The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Calculus For Biology and Medicine (Calculus for Life Sciences Series) was written by Patricia and is associated to the ISBN: 9780321644688. Since 82 problems in chapter 4.2: The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials have been answered, more than 5315 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 4.2: The Power Rule, the Basic Rules of Differentiation, and the Derivatives of Polynomials includes 82 full stepbystep solutions.

Absolute minimum
A value ƒ(c) is an absolute minimum value of ƒ if ƒ(c) ? ƒ(x)for all x in the domain of ƒ.

Angle
Union of two rays with a common endpoint (the vertex). The beginning ray (the initial side) can be rotated about its endpoint to obtain the final position (the terminal side)

Arccosine function
See Inverse cosine function.

Bar chart
A rectangular graphical display of categorical data.

Common difference
See Arithmetic sequence.

Definite integral
The definite integral of the function ƒ over [a,b] is Lbaƒ(x) dx = limn: q ani=1 ƒ(xi) ¢x provided the limit of the Riemann sums exists

Demand curve
p = g(x), where x represents demand and p represents price

Elements of a matrix
See Matrix element.

Fibonacci sequence
The sequence 1, 1, 2, 3, 5, 8, 13, . . ..

Geometric sequence
A sequence {an}in which an = an1.r for every positive integer n ? 2. The nonzero number r is called the common ratio.

Line of symmetry
A line over which a graph is the mirror image of itself

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

Linear correlation
A scatter plot with points clustered along a line. Correlation is positive if the slope is positive and negative if the slope is negative

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Outliers
Data items more than 1.5 times the IQR below the first quartile or above the third quartile.

PH
The measure of acidity

Quotient rule of logarithms
logb a R S b = logb R  logb S, R > 0, S > 0

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

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

Trichotomy property
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
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