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# Derivatives

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### First Partial Derviatives

See attachment. Compute the first partial derivatives of the function: W = 4x^3 y^2 - 3xyz + 7yz^2.

### Compute Derivatives

See attachment.

### Determing Rate of Change using Chain Rule

The radius of a right circular cone is increasing at a rate of 1.6in/s while its height is decreasing at a rate of 2.5 in/s. At what rate is the volume of the cone changing when the radius is 120in and the height is 140in?

### Derivatives

See attachment for equations 1) determine the interval(s) where the function is increasing and the interval(s) where it is decreasing. 2) determine the interval(s) where the function is increasing and the interval(s) where it is decreasing. 3) Find the relative maxima and relative minima, if any, of the following functi

### Scheduling

See attached for proper formatting Rank the Critical ratio sequencing rules on the three evaluation criteria of average flow time, average number of jobs in the system, and average job lateness for the information below. (Do not evaluate shortest processing time or first-come first-served). A production planner must deci

### Finding the Second Partial Derivatives

Find the second partial derivatives of: z = x / (x+y).

### Cowling's rule

Cowling rule is another method for determining the dosage of a drug to prescribed to a child. For this rule, the formula d=D(a+1) ------ 24 gives the child's dosage d, Where D is the adult dosage and a is the age of the child in years. If the adult dosage of a drug is 600 milligrams and a doctor uses this formula to

### Applications of the Derivative

Please see the attached file for the fully formatted problems. For the function y= sq root (x2 - 9) (i) Find the slope of the tangent line to the function at the point (5, 4). (ii) Find the equation of the normal line at the point (5, 4). 2. A ladder 10 m long rests on horizontal ground and leans against a vertical wal

### Graphs and derivatives

See attached problems The graph of the first derivative of f is shown....

### Critical points

Attached problems no#2 and 10 Find the intervals on which f is increasing or decreasing....

### Critical points

Please help with attached problems #2 and #10 thanks Find the intervals on which f is increasing or decreasing. Find the local maximum and minimum values of f. Find the intervals of concavity and inflection points.

### application of derivative

With a yearly inflation rate of 7%, prices are given by P=p(1.05)^t, where p is the price in dollars when t=0 and t is the time in years. Suppose p=1. How fast (in cents/ year) are prices rising when t=12? Find f'(x) and f''(x) if f(x)=(4x^2+12)(3x-1)

### Derivatives Square Roots

Find the derivative of w(x)=tan(x^4) Find dy/dx of (the square root of x + square root of y)=36

### Derivatives and Change

Let xy^2+2y(x+2)^2+2=0 a) if x changes from -2.00 to -2.01 and y>0, approximately how much does y change? b)if x changes from -2.00 to -2.01 and y<0, approximately how much does y change?

### Derivatives of exponential functions ...

Find the value of c in Figure 3.12 (picture attached), where the line l tangent to the graph of y = 2x at (0, 1) intersects the x-axis. Give your answer correct to 2 decimal places. Find the derivative of the function below. f(x) = e^2 + x^e

### Market Share Analysis

This table presents units sold and market share data for the Personal Computers Industry (first figure for each company is units, second is revenue). E-Top--10,000--7,500,000 CompEZ--15,000--12,000,000 BEST--2,000--1,700,000 Moonwalk--8,000--8,000,000 CompBrain--8,000--12,000,000 Market Total--43,000 units--41,200,000

### Homogeneous Functions and Partial Derivatives

Each function f is homogeneous of degree n, that is f satisfies the equation f(tx,ty)= t^n f(x,y) for all t, where n is a positive integer and f has continuous second-order partial derivatives. Verify that f satisfies the given equation. See attached page for equation.

### Partial derivatives

See attached page for problem

### Example of Working with Implicit Differentiation

See attached page for equation and problem.

### Finding Rate of Change in a Given Direction

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1,2,2) is 120 degrees. Find the rate of change of T at (1,2,2) in the direction toward the point (2,1,3) Show that at any point in the ball the direction of

### Find the directional derivative of f

Find the directional derivative of f at the given point in the direction indicated by the angle f(x,y)= sin(x+2y), (4,-2), theta= -2pi/3

### Example of Using Chaine Rule to Find a Derivative

Z= ln(x+y^2), x=squareroot (1+t), y= 1 + squareroot (t).

### Finding second derivatives of given functions

Find the second derivative of the following two functions: a) y - e^x sin x b) y - sin 2x + cos 3x Thank you for the help!

### Using the Chain rule for derivatives in higher dimension

Let f(u,v,w) = (eu-w, cos(v+u)+sin(u+v+w)) and g(x,y) = (ex, cos(y-x), e-y). Calculate f o g and D(f o g)(0,0).

### Find the indicated partial derivative.

F(x,y,z)= x^5 + (x^4)(y^4)(z^3) + yz^2; f(xyz)

### Partial Derivatives. Find dz/dx and dz/dy

1.)z= f(x)g(y) 2.)z= f(xy) 3.)z= f(ax + by)

### Find the first partial derivatives of the function.

1.) g(x,y)= ln(x + ln(y))

### Find the indicated partial derivatives.

1.)f(x,y)= sin(y-x); df/dx(3,3) 2.)z= (x^3 + y^3)/(x^2 + y^2); dz/dx, dz/dy 3.)xyz= cos(x + y + z); dz/dx, dz/dy

### First and second derivatives problems

Find the first and second differentials of the following: f= ln(cosX-sinX)

### Differentiation

Please see attachment