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# Derivatives

### 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 Evaluated

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 − x)(1 − 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.

### Derivatives : Product and Quotient Rules

Please see the attached file for the fully formatted problems.

### Rate of Change Functions

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, 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 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

### Derivatives and Limits

Differentiate the function with respect to : 1) 2) 3) 4) 5) Determine Limit 6)

### Find dy/dx given x and y.

Find dy/dx, given x = t^2 and y = t^3.

### 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.

### Implicit Differentiation Functions

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.

### 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

### Linear Functionals, Continuous Derivatives and Scalars

Note that in problem 2, <x,l_1> = l_1(x), etc Please see the attached file for the fully formatted problems.

### Differentiation Function Solved

Find f'(x) f(x) = 1/ sq.rt. x

### 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 and Rate of Change: Increasing Radius

An oil spill has a shape of a circle and it is growing at a rate of 100 m² per second. At what rate is the radius increasing when it is 500 m?

### 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, Epsilon-Delta Proof of Continuity and Integrals

A) If x, y > 0, then ln x - ln y = ln x ¯¯¯¯ ln y b) If f'(a) = 0 and f"(a) = 0, then the function f does not have an extreme point at x = a. c) For every real number x, we have ln(e^x²-¹) = (x - 1)(x + 1) (e

### 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)