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Derivatives

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

Calculus - Derivatives - Composite Rule - IVP

Use composite and product rule to differentiate. See attached file for full problem description. Solve the Initial value problem ........ For full problem description, please see the attached problem file.

Partial Derivative Explanation

Please see the attached file for the fully formatted problems. where The partial derivative of c with respect to S is the following: I do not understand how to get to this solution. I do not understand how to get the partial with respect to S out of the distributions N(d1¬) and N(d2). Please show ste

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

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)

Find f' (x)

Please explain the steps and the solution, thank you: Find f' (x) of f(x) = sin (e^3x) (^ means exponent)

Derivatives: Finding Functions

Please explain the steps and solution, thank you: Find two functions f and g such that the derivatives f' (x) = g' (x) = 3x^2 and such that f (x) - g (x) = 7 (^ means exponent)

Find f'(x)

Please explain the solution, thank you: Find f'(x) of f(x) = sin (e^3x) (^ means exponent)