 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 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 21548 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.

Bounded
A function is bounded if there are numbers b and B such that b ? ƒ(x) ? B for all x in the domain of f.

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Cone
See Right circular cone.

Conjugate axis of a hyperbola
The line segment of length 2b that is perpendicular to the focal axis and has the center of the hyperbola as its midpoint

Convergence of a series
A series aqk=1 ak converges to a sum S if imn: q ank=1ak = S

Degree
Unit of measurement (represented by the symbol ) for angles or arcs, equal to 1/360 of a complete revolution

Event
A subset of a sample space.

Hyperbola
A set of points in a plane, the absolute value of the difference of whose distances from two fixed points (the foci) is a constant.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Principle of mathematical induction
A principle related to mathematical induction.

Proportional
See Power function

Second quartile
See Quartile.

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

Sequence
See Finite sequence, Infinite sequence.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Solve an equation or inequality
To find all solutions of the equation or inequality

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.