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Derivatives

Solve: Derivatives, Chain Rule and Rate of Change

Please assist me with understanding the following questions: 1. A glider is flying along the line y = - (1/3)x + 100. Its horizontal shadow is moving at 10 m/s. How fast is the glider approaching the origin (0,0) at the time when it is located at (-30, 110)? 2. Boyle's Law states that when a sample of gas is compressed a

Implicit Differentiation Variables

Please help & please show step-by-step, thx, appreciate it. Below are notes my instructor gave for this assignment that are relative and important. The problems are below. There is 1 problem at the bottom of the page. Thank you. When differentiating keep in mind the variable with respect you differentiate. For example, the

Description of Cramer's rule

Solve the following linear system for x using Cramer's rule. Show work. x + 2y - 3z = -22 2x - 6y + 8z = 74 -x - 2y + 4z = 29

Local Extrema and Volume of a Solid of Revolution

Please see attached file for full problem description. The graph of the derivative of a function f is shown below. (a) Over what intervals is f(x) increasing? decreasing? Why? (b) At what x values does f(x) have a local maximum? Why? (c) At what x values does f(x) have a local minimum? Why? (d) Sketch a possible

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.

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

Derivatives and Rates of Change

Please see the attached file for the fully formatted problems. 4. Go to a financial website (for exmaple, finance.google.com), 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 Rate of Change Explanation

A conical tank has a radius of 5 feet and a height of 10 feet. Water runs into the tank at the constant rate of 2 cubic feet per minute. How fast is the water level rising when the water is 6 feet deep? Round your answer to the nearest hundredth.

Find the Derivatives

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

Derivatives for Left-Handed Widget Manufacturing

See attached file for full problem description. The world's only manufacturer of left-handed widgets has determined that if q left handed widgets are manufactured and sold per year at price p, then the cost function is C = 8000 + 40q and the manufacturer's revenue function is R = pxq. The manufacturer also knows that the dema

Derivatives : Maximizing Profit

Acme can produce DVD players at a cost of $140 each and market analysis estimates that if the players are sold at x dollars apiece, consumers in a region will buy approximately 2000e^-0.01x machines per week. At what price should the players be sold to maximize profit? $240 $265 $340

Geometric Mean Rate of Increase

A recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power. You would need to make $44,771 if the inflation rate jumped to 6 percent. Confirm that these statements are accurate by finding the geo

Derivative and 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: Derivatives

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.

Derivative of Limits

Please 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

Derivatives of Functions

Find and simplify derivatives of the functions: a) y = cos x ¯¯¯¯¯¯¯ x^2+e^2x b) y = ln((x^2 + 1)(cos x)) (^ means exponent and e^2x, 2x is the exponent).

Derivatives of Trigonometric Functions : Chain Rule

Use chain rule to verify that every function of the form y = a sin (5t) + b cos (5t) is a solution to the differential equation d^2y/dt^2 = -25y. Then use this fact to find the solution which also satisfies the initial conditions: y(0) = 3 and y'(0) = 0 (^ means exponent and d^2y is over dt^2)

Functions : Derivatives, Areas of Increase and Extrema

Suppose f(x) = ln(2 + cos x) on the interval (0, 2pi). a) Calculate f' (x) and f" (x). b) Find the interval(s) on which the function f is increasing. c) Find all extreme values of f and the values of x at which they occur. d) Find the interval(s) on which the function f is concave up?

Functions : Derivatives, Areas of Increase and Extrema

Suppose f(x) = ln(2 + cos x) on the interval (0, 2pi). a) Calculate f' (x) and f" (x). b) Find the interval(s) on which the function f is increasing. c) Find all extreme values of f and the values of x at which they occur. d) Find the interval(s) on which the function f is concave up?

implicit differentiation and explicit function

Please explain the steps and solution, thanks: The equation 4x^2y - 3y = x^3 implicitly defines y as a function of x. a) use implicit differentiation to find dy/dx. b) write y as an explicit function of x and compute dy/dx directly.

Chain rule to find derivatives

Please explain the steps and solution: Calculate derivatives of the function h (x) = ln (x^3) - ln (^2) (^ means exponent)