Explore BrainMass


Finding the first and second derivative.

Y= (1 + 1/x)^1/4 Got the 1st derivative to be Y'= 1/4 (1+1/x)^-3/4 * (-1x)^-2 Is that correct? Now I need the 2nd derivative, I am completely lost on this. Please work out clearly.

Trigonometric Derivatives

Find derivatives (and check your answer with the differentiator from Wolfram) d/dx{(secx(tanx+cosx)}

Tangent Lines

6. Graph y=sinx + cosx restricted to 0<=x<=pi/2. Locate the points on the graph at which the tangent line appears to have slope zero. Then find those x, 0<=x<=pi/2 , for which the function f(x)=sinx+cosx has a horizontal tangent line. (You need to solve the equation: f' (x)=0 for 9<x< pi/2 )

Find derivatives

1- 4 Find derivatives. 1. d/dx(sinx + cosx + e^x) 2. d/dx(tanx - secx) 3. d/dx{secx9tanx + cosx)} 4. d/dx(cot x) sub|x=pi/4

Quotient Rule

Apply the quotient rule to f(x) = p(x)/q(x) and show that f&#8242;(0) = p&#8242;(0)/q(0) if p(0) = 0. Hence evaluate f&#8242;(0), wheref(x) =xe^2x/(2 &#8722; x)(1 &#8722; x)^2

Differentiation Proof

By following the proof that d/dx e^x , show that for f(x) = a^x, d/dx a^x = f'(o)a^x.

Rate of Change

A(t) is just the function that you choose to use from the world clock site's photo. Pick any quantity that surprises you and call it . Then assuming that the clock is correct, explain in a paragraph how you calculate the change of per second. Then the change of A(t) per day. For instance, it could be anything, such as tempe

Derivatives and Rates of Change

Please see the attached file for the fully formatted problems. 4. Go to a financial website (for exmaple,, pick your favorite stock. By denote the price at which the stock was exchanged at time where is measured in seconds from last Friday midday. What does mean? What does mean? Estimate the average rat

Derivatives and Instantaneous Rates of Change

Please see the attached file for the fully formatted problems. 1. Let where . Tabulate the change of over the intervals(i) , (ii) , (iii) , (iv) , (v) . Estimate the instantaneous rate of change of at . 2. Use the limit definition of rate of change to calculate how quickly is changing at


If 2x^2 + 3xy = 12x + 5y, what is dy/dx? I put the x's on one side and got: 2x^2 - 12 x = 3xy +5y then 4x - 12 = 3y + 5, but I'm not sure how to get a dy and dx.

Find the Derivatives

Find the derivative of f(x) = (x^2 -1)^3 /(2x^2). Find the 12th derivative of f(x) = cos x.

Partial Derivatives : Maxima and Minima

In page number 139, I need THEOREM I (Please mention each and every step). In page Number 141, I need Example 3 ( Please mention each and every step). Advance Calculus, Author: - Taylor & Menon - page 139, and 141

Finding Partial Derivatives

Please see the attached file for the fully formatted problems. Given * : From *, it is known that: and . I know that the solutions of the following derivatives are these: Show each step to get to the given solutions of 1), 2), and 3).

Derivatives, Rate of Change and Properties of Functions

1. A spherical bubble is expanding at a rate of 60pi cm3. How fast is the surface area of the bubble expanding when the radius of the bubble is 4 cm? 2. Identify the following features of the graphs: -the intercepts -domain and range -any symmetry -vertical and/or horizontal asymptotes -the coordination of any stat

Average value

Please choose the correct answer: 2. If f(x) = (x + ln x)^2 , then f '(x) = (2/x)(x + 1)(x + ln x) (2/x)(1 + ln x) (2/x)(x + 2)(x + 2 ln x) (2/x)(x + 2 ln x) (4/x)(1 + 2 ln x) (4/x)(x + 2)(x + 2 ln x) none of these Q#11. The average value of f(x) =

Calculus Questions

Q#1) Find the equation of the tangent line to y = 2 ln x at the point where x = 8. Q#2) If f(x) = (x + 2 ln x)^2 , then f '(x) = Q# 3) f(x) =ln[ (2x^3)(e^(4x + 3)], then f ''(x) = Note: (4x+3) whole power of e


I need to find the derivative of 9-t^2 using the formula: f(a + h) - f(a) lim _____________ h = the change in a h->0 h Can someone explain how to do this problem in enough detail that I can use the explanation to solve other problems?

Derivatives and Rate of Change : Drug Elimination Rate

Please do Part B. PROBLEM STATEMENT: The concentration in the blood resulting from a single dose of a drug decreases with time as the drug is eliminated from the body. In order to determine the exact pattern that the decrease follows, experiments are performed in which drug concentrations in the blood are measured at various

Derivatives : Maximizing Area and Minimizing Cost

A farmer wants to fence a rectangular area as inexpensively as possible. Assume that fencing materials cost $1 per foot. a) Suppose that $40 is available for the project. How much area can be enclosed? b) Suppose that 100 square feet must be enclosed. What is the least possible cost? c) Discuss the relation betwee