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# Derivatives

### First and second partial derivatives

The problem is: Z = X COS Y - Y COS X I am to find all of the first and second partial derivatives of this problem. Will you please solve this problem in detail so that I may use the method you show to solve similar problems?

### Derivatives and tangents

Use the definition of the derivative to find f '(x) given f(x)=^/Â¯x Write an equation of the line tangent to the curve at the point P(-1, 7). Express the answer in the form ax + by = c. y= 5/x^2-2/x^3 Write the equation of the line tangent to the curve at the point P where x = 4. Write the equation in the f

### Definition of the Derivative and Maximum Value

Use the definition finition of the derivative to find f'(x) given f(x) = sqrt(x). y(t) = -16t^2 + 80t + 96 A ball thrown vertically upward at time t = 0s with initial velocity 80 ft/s and with initial height function in fig 2.1. a) What is the maximum height attained by the ball? b) When and with what impact speed d

### Minimizing Surface Area

A container company is going to construct a shipping container of volume 12 ft3 with a square bottom and a square top. The cost of the top and sides is \$2 per square foot and for the bottom is \$3 per square foot. What dimensions will minimize the cost of the container.

### Fifth Derivative

Compute the fifth derivative of 1 / g(x). You can use Faa di Brunos formula if you wish.

### Maximum and Minimum Values of Functions

The Association of Economists Least Likely to Win Any Awards (AELLWAA) was founded 20 years ago.... Find the maximum and minimum years of membership for the attached equation.

### minimizing the average cost

A domestic auto producer is facing intense competition in the US market from Asian imports. The CFO decides that the solution is to produce at the point at which average cost is minimized, i.e. where TC/Q is at a minimum. The firm's cost structure is given by: TC={(1/3Q)^3}-{(100Q)^2}+20,000Q Calculate the average cost-min

### Antiderivatives Differentiation Verified

? Guess an antiderivative of and verify by differentiation that your guess is correct. ? Guess an antiderivative of and verify by differentiation that your guess is correct. ? Guess an antiderivative of and verify by differentiation that your guess is correct. ? Guess an antiderivative of and verify by differentiat

### Derivatives of Exponential Functions

Please see the attached file for the fully formatted problems.

### Find the partial derivatives ..

Please see attachment. 4.10 Find the partial derivatives with respect to x, y, and z of the following functions: (a) f(x,y,z) = ax^2 +bxy + cy^2 (b) g(x,y,z) = sin(axyz^2), (c) h(x,y, z) = ax^(xy/z^2). where a, b, and c are constants

### L'Hospital's Rule

Please see the attached file for the fully formatted problems. 17 L`Hospital`s Rule These are instructions from my professor he wants us to use this form & these rules to do the problems. He wants us to follow these sepd. Please help, I appreciate it. There are 3 problems in this set and 3 pages. thx Note this is not the Q

### L'Hospital's Rule - Limit Laws

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### Real Functions of Real Variable, Continuity

Let f:R->R satisfy |f(t)-f(x)|<=|t-x|^2 for any t,x. Prove that (f) is constant.

### Solve: Decreasing Functions

Determine the intervals on which the function is increasing and intervals on which the function is decreasing. Check your answers by graphing the corresponding functions. - Please view the attachment for the rest of the solution. Question: Determine the intervals on which the function is increasing and intervals on whic

### Limits and Derivatives : Definition of the Derivative

Please see the attached file for the fully formatted problems.

### Differentiability and Derivatives

Please see the attached file for the fully formatted problems. 1. Let be a positive number and defined by Determine all values of k such that f is differentiable at 0. What is f' (0) then?

### Using logarithmic differentiation to find derivatives of equations.

1. Use logarithmic differentiation to find [see attachment]. 2. Use logarithmic differentiation to find [see attachment]. 3. Use logarithmic differentiation to find [see attachment]. Please see attachment.

### Derivatives and Extreme Values

1. Find the maximum and minimum values of defined on the interval . 2. Find the maximum and minimum values of defined on the interval . 3. Find the maximum and minimum values of on the interval . Then graph the function to check your answers. Please see the attached file for the fully formatted problems.

### 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

### Definition of the Derivative & Questions

Please see the attached file for the fully formatted problems. Key points: The derivative of at is the instantaneous rate of change of and it is denoted by . If we let , we obtain an equivalent formula that is at times more convenient to use in problems. A function for which the exists is called differentiabl

### 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

### Derivatives : Chain Rule, Leibnitz Notation and Tangent Lines

Please see the attached file for the fully formatted problems. 12. Show that satisfies the equation . 13. Let be a constant. Find and show that satisfies the equation . Note the notation: . 14. Find an equation of the tangent line to at the point . Note the notation: .

### Derivatives : Chain Rule, Leibnitz Notation and Inner and Outer Functions

Please see the attached file for the fully formatted problems. The Chain Rule states how to differentiate composite functions If and be differentiable, then the derivative of the composite function is In Leibnitz notation, if and , then . For example, or The derivative of the exponential function is

### 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.

### Trigonometric Derivatives

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

### Derivatives of Trigonometric Functions

D/dx {(secx(tanx-scex)}

### Derivatives and 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 )