Calculus Volume 1 18th Edition solutions

Calculus Volume 1 18
For the following exercises, given y = f(u) and u = g(x), find \(\frac{d y}{d x}\) by using Leibnizs notation for the chain rule: \(\frac{d y}{d x}=\frac{d y}{d u} \frac{d u}{d x} .\). y = 3u -6, \(u=2 x^{2}\) Text Tran

Calculus Volume 1 18
For the following exercises, given y = f(u) and u = g(x), find \(\frac{d y}{d x}\) by using Leibnizs notation for the chain rule: \(\frac{d y}{d x}=\frac{d y}{d u} \frac{d u}{d x} .\). \(y=6 u^{3}\), u=7x-4 Text Transcr

Calculus Volume 1 18
For the following exercises, given y = f(u) and u = g(x), find \(\frac{d y}{d x}\) by using Leibnizs notation for the chain rule: \(\frac{d y}{d x}=\frac{d y}{d u} \frac{d u}{d x} .\). y= sin u, u=5x-1 Text Transcriptio

Calculus Volume 1 18
For the following exercises, given y = f(u) and u = g(x), find \(\frac{d y}{d x}\) by using Leibnizs notation for the chain rule: \(\frac{d y}{d x}=\frac{d y}{d u} \frac{d u}{d x} .\). y= cos u, \(u=\frac{-x}{8}\) Text

Calculus Volume 1 18
For the following exercises, given y = f(u) and u = g(x), find \(\frac{d y}{d x}\) by using Leibnizs notation for the chain rule: \(\frac{d y}{d x}=\frac{d y}{d u} \frac{d u}{d x} .\). y= tan u, u=9x+2 Text Transcriptio

Calculus Volume 1 18
For the following exercises, given y = f(u) and u = g(x), find \(\frac{d y}{d x}\) by using Leibnizs notation for the chain rule: \(\frac{d y}{d x}=\frac{d y}{d u} \frac{d u}{d x} .\). \(y=\sqrt{4 u+3}\), \(u=x^{2}-6 x\)

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=(3 x-2)^{6}\) Text Transcription: dy/dx y= (3x-2)^6

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=\left(3 x^{2}+1\right)^{3}\) Text Transcription: dy/dx y=(3x^2

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=\sin ^{5}(x)\) Text Transcription: dy/dx y= sin^5 (x)

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=\left(\frac{x}{7}+\frac{7}{x}\right)^{7}\) Text Transcription:

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. y= tan(sec x) Text Transcription: dy/dx

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=\csc (\pi x+1)\) Text Transcription: dy/dx y= csc(pi x+1)

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=\cot ^{2} x\) Text Transcription: dy/dx y= cot^2 x

Calculus Volume 1 18
For each of the following exercises, a. decompose each function in the form y = f(u) and u = g(x), and b. find \(\frac{d y}{d x}\) as a function of x. \(y=-6 \sin ^{-3} x\) Text Transcription: dy/dx y= -6sin^-3 x

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=\left(3 x^{2}+3 x-1\right)^{4}\) Text Transcription: dy/dx y=(3x^2+3x-1)^4

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=(5-2 x)^{-2}\) Text Transcription: dy/dx y=(5-2x)^-2

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=\cos ^{3}(\pi x)\) Text Transcription: dy/dx y=cos^3 (pi x)

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=\left(2 x^{3}-x^{2}+6 x+1\right)^{3}\) Text Transcription: dy/dx y=(2x^3 -x^2 +6x+1)^3

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=\frac{1}{\sin ^{2}(x)}\) Text Transcription: dy/dx y= 1/sin^2 (x)

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=(\tan x+\sin x)^{-3}\) Text Transcription: dy/dx y=(tan x + sin x)^-3

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=x^{2} \cos ^{4} x\) Text Transcription: dy/dx y=x^2 cos^4 x

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. y = sin(cos7x) Text Transcription: dy/dx

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=\sqrt{6+\sec \pi x^{2}}\) Text Transcription: dy/dx y=sqrt 6+sec pix^2

Calculus Volume 1 18
For the following exercises, find \(\frac{d y}{d x}\) for each function. \(y=\cot ^{3}(4 x+1)\) Text Transcription: y= cot^3 (4x+1)

Calculus Volume 1 18
Let \(y=[f(x)]^{3}\) and suppose that f ?(1) = 4 and \(\frac{d y}{d x}=10\) for x = 1. Find f(1). Text Transcription: y=[f(x)]^3 dy/dx =10

Calculus Volume 1 18
Let \(y=\left(f(x)+5 x^{2}\right)^{4}\) and suppose that f(?1) = ?4 and \(\frac{d y}{d x}=3\) when x = ?1. Find f ?(?1) Text Transcription: y=[f(x)+5x^2]^4 dy/dc=3

Calculus Volume 1 18
Let \(y=(f(u)+3 x)^{2}\)and \(u=x^{3}-2 x\). If f(4) = 6 and \(\frac{d y}{d x}=18\) when x = 2, find f ?(4). Text Transcription: y= (f(u) + 3x)^2 u=x^3 -2x dy/dx =18

Calculus Volume 1 18
[T] Find the equation of the tangent line to \(y=-\sin \left(\frac{x}{2}\right)\) at the origin. Use a calculator to graph the function and the tangent line together. Text Transcription: y= -sin(x/2)

Calculus Volume 1 18
[T] Find the equation of the tangent line to \(y=\left(3 x+\frac{1}{x}\right)^{2}\) at the point (1, 16). Use a calculator to graph the function and the tangent line together. Text Transcription: y=(3x+ 1/x)^2

Calculus Volume 1 18
Find the x -coordinates at which the tangent line to \(y=\left(x-\frac{6}{x}\right)^{8}\) is horizontal Text Transcription: y=(x- 6/x)^8

Calculus Volume 1 18
[T] Find an equation of the line that is normal to \(g(\theta)=\sin ^{2}(\pi \theta)\) at the point \(\left(\frac{1}{4}, \frac{1}{2}\right)\). Use a calculator to graph the function and the normal line together. Text T

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. h(x) = f (g(x)); a = 0

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. h(x) = g( f(x)); a = 0

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. \(h(x)=\left(x^{4}+g(x)\right)^{-2}\); a=1 Text Transcription: h(x)= (x^4 + g(x))^-2

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. \(h(x)=\left(\frac{f(x)}{g(x)}\right)^{2}\); a=3 Text Transcription: h(x) = (f(x)/g(x))^2

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. h(x) = f(x + f(x)); a = 1

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. \(h(x)=(1+g(x))^{3}\); a=2 Text Transcription: h(x)=(1+g(x))^3

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. \(h(x)=g\left(2+f\left(x^{2}\right)\right)\); a=1 Text Transcription: g(x)= g(2+f(x^2))

Calculus Volume 1 18
For the following exercises, use the information in the following table to find h?(a) at the given value for a. h(x) = f (g(sinx)); a = 0

Calculus Volume 1 18
[T] The position function of a freight train is given by \(s(t)=100(t+1)^{-2}\), with s in meters and t in seconds. At time t = 6 s, find the trains a. velocity and b. acceleration. c. Using a. and b. is the train speeding up or slowing down?

Calculus Volume 1 18
[T] A mass hanging from a vertical spring is in simple harmonic motion as given by the following position function, where t is measured in seconds and s is in inches: \(s(t)=-3 \cos \left(\pi t+\frac{\pi}{4}\right)\ a. Determine the position of the spring at t = 1.5 s. b. Find the veloci

Calculus Volume 1 18
[T] The total cost to produce x boxes of Thin Mint Girl Scout cookies is C dollars, where \(C=0.0001 x^{3}-0.02 x^{2}+3 x+300\). In t weeks production is estimated to be x = 1600 + 100t boxes. a. Find the marginal cost C?(x). b. Use Leibnizs notation for the chain rule, \(\frac{d C}{d t}=\f

Calculus Volume 1 18
[T] The formula for the area of a circle is \(A=\pi r^{2}\) , where r is the radius of the circle. Suppose a circle is expanding, meaning that both the area A and the radius r (in inches) are expanding. a. Suppose \(r=2-\frac{100}{(t+7)^{2}}\) where t is time in seconds. Use the chain rule \(\fr

Calculus Volume 1 18
[T] The formula for the volume of a sphere is \(S=\frac{4}{3} \pi r^{3}\), where r (in feet) is the radius of the sphere. Suppose a spherical snowball is melting in the sun. a. Suppose \(=\frac{1}{(t+1)^{2}}-\frac{1}{12}\) where t is time in minutes. Use the chain rule \(\frac{d S}{d t}=\frac{d

Calculus Volume 1 18
[T] The daily temperature in degrees Fahrenheit of Phoenix in the summer can be modeled by the function \(T(x)=94-10 \cos \left[\frac{\pi}{12}(x-2)\right]\), where x is hours after midnight. Find the rate at which the temperature is changing at 4 p.m.

Calculus Volume 1 18
[T] The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled by the function \(D(t)=5 \sin \left(\frac{\pi}{6} t-\frac{7 \pi}{6}\right)+8\), where t is the number of hours after midnight. Find the rate at which the depth is changing at 6 a.m.