 3.7.1: Explain why the natural logarithmic function y ln x is used much mo...
 3.7.2: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.3: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.4: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.5: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.6: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.7: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.8: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.9: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.10: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.11: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.12: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.13: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.14: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.15: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.16: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.17: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.18: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.19: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.20: 220 Differentiate the function. 2. fsxd x ln x 2 x 3. fsxd sinsln x...
 3.7.21: 2122 Find y9 and y99. 21. y x 2 lns2xd 22. y ln x x 2
 3.7.22: 2122 Find y9 and y99. 21. y x 2 lns2xd 22. y ln x x 2
 3.7.23: 2324 Differentiate f and find the domain of f. 23. fsxd x 1 2 lnsx ...
 3.7.24: 2324 Differentiate f and find the domain of f. 23. fsxd x 1 2 lnsx ...
 3.7.25: 2526 Find an equation of the tangent line to the curve at the given...
 3.7.26: 2526 Find an equation of the tangent line to the curve at the given...
 3.7.27: If fsxd ln x x 2 , find f9s1d.
 3.7.28: Find equations of the tangent lines to the curve y sln xdyx at the ...
 3.7.29: Dialysis The project on page 458 models the removal of urea from th...
 3.7.30: Genetic drift A population of fruit flies contains two genetically ...
 3.7.31: Carbon dating If N is the measured amount of 14C in a fossil organi...
 3.7.32: Let fsxd logbs3x 2 2 2d. For what value of b is f9s1d 3
 3.7.33: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.34: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.35: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.36: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.37: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.38: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.39: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.40: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.41: 3341 Use logarithmic differentiation to find the derivative of the ...
 3.7.42: Predatorprey dynamics In Chapter 7 we study a model for the popula...
 3.7.43: 4348 Find the derivative of the function. Simplify where possible. ...
 3.7.44: 4348 Find the derivative of the function. Simplify where possible. ...
 3.7.45: 4348 Find the derivative of the function. Simplify where possible. ...
 3.7.46: 4348 Find the derivative of the function. Simplify where possible. ...
 3.7.47: 4348 Find the derivative of the function. Simplify where possible. ...
 3.7.48: 4348 Find the derivative of the function. Simplify where possible. ...
 3.7.49: 4950 Find the limit. 49. lim x l` arctansex d 50. lim xl01 tan21 sln
 3.7.50: 4950 Find the limit. 49. lim x l` arctansex d 50. lim xl01 tan21 sln
 3.7.51: Find y9 if y lnsx 2 1 y 2 d.
 3.7.52: . Find y9 if xy yx .
 3.7.53: Find a formula for f snd sxd if fsxd lnsx 2 1
 3.7.54: Find d 9 dx 9 sx 8 ln x
 3.7.55: Use the definition of derivative to prove that lim xl0 lns1 1 xd x
 3.7.56: how that limn l` S1 1 x n D n ex for any x
Solutions for Chapter 3.7: Derivatives of the Logarithmic and Inverse Tangent Functions
Full solutions for Biocalculus: Calculus for Life Sciences  1st Edition
ISBN: 9781133109631
Solutions for Chapter 3.7: Derivatives of the Logarithmic and Inverse Tangent Functions
Get Full SolutionsBiocalculus: Calculus for Life Sciences was written by and is associated to the ISBN: 9781133109631. Since 56 problems in chapter 3.7: Derivatives of the Logarithmic and Inverse Tangent Functions have been answered, more than 27379 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.7: Derivatives of the Logarithmic and Inverse Tangent Functions includes 56 full stepbystep solutions. This textbook survival guide was created for the textbook: Biocalculus: Calculus for Life Sciences , edition: 1.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)ยท(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Solvable system Ax = b.
The right side b is in the column space of A.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.