Explore BrainMass


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,, 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

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

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

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?

Equation of the Line Tangent to the Curve

Hi, this was your response since dy/dx means the slope of a tangent to the curve at a certain point there fore dy/dx= (3 x^2)- (6*2*x^1) dy/dx = (3x^2) - (12x) Equation of the line tangent to the curve= dy/dx = 3x^2 - 12x Thanks Ramesh but can you please explain further how you got dy/dx= (3 x^2)- (6*

Finding the Derivatives in Calculus

Q#8. For f(x)=2-5X^2, Find: i) f`(x). Answers: a. -5x b. -10x c. -10x d. 0 Q#9. Consider f(x)=3-4*Square root(X) i) Find f`(x) Answers: a. - square root of X / 2 b. - 4 / square root of X c. -2/square root of x d. -8 / Square root of x. Q#10. Consider f(x)=3x/x+9 i) find f`(x) Q#7. A per

Derivatives : Velocity and Displacement

27. A ball is thrown straight downward from the top of a tall building. The initial speed of the ball is 10 m/s. It strikes the ground with a speed of 60 m/s. How tall is the building? Answer: y0 = 178.57 m 35. A stone is dropped from rest at an initial height h above the surface of the Earth. Show that the speed wit

Proofs: Polar Coordinates

Please view the attached file for proper formatting on the following questions regarding polar coordinates. 1. Consider the polar coordinates: x = rcos(theta) y = rsin(theta) Questions a) to e) can be seen in the attachment.

Derivatives and Rate of Change

Early one morning it began to snow at a constant rate. At 7 AM a snowplow set off to clear a road. By 8 AM it had traveled 2 miles but it took two more hours for the snowplow to go another 2 miles. Assuming that the snowplow clears snow from the road at a constant rate (in cubic feet per hour), at what time did it start to snow?

Derivatives, Rate of Change and the Fundamental Theorem of Calculus

1. The resale value of a certain industrial machine decreases at a rate that depends on its age. When the machine is t years old, the rate at which its value is changing is -960e^-t/5 dollars per year. a) Express the value of the machine in terms of its age and initial value. b) If the machine was originally worth $5,200,

Critical Points and Continuous Second Derivatives

2. Suppose (0, 2) is a critical point of a function g with continuous second derivatives. In each case, what can you say about g? (a) gxx(0, 2) = ? 1, gxy(0. 2) = 6, gyy(0, 2) = 1 Please see the attached file for the fully formatted problems.

Curve Sketching

See attached file for full problem description. 1.Boat A is sailing south at 24 km/h while boat B, which is 48 kilometres due south of A, is sailing east at 18km/h. a)At what rate are they approaching or separating one hour later? b)When do they cease to approach on another and how far apart are they at this time? c)What

Laws of Logarithms and derivative

Please see the attached file for full description 1.Evaluate the following logarithms. a)log22log55 b)log23200-2log210 2.Solve the following logarithmic equation. log25=log2(x+32)-log2x 3.Determine the derivative of each of the following functions. a)y=ln(x2+3x+4) b)y=logx2 c)y=lnx^2/(3x-4)^3 d)y=2x3e4x

Derivatives : Demand and Cost Functions

The marketing research department for a computer company used a large city to test market their new product. They found that the demand equation was p= 1296-0.12 x^2. If the cost equation is C = 830+396 x, find the number of units that will produce maximum profit. I do not have a price per unit, only the above cost equatio

Thermodynamics Equation

Thermodynamics texts use the relationship (dy/dx)(dz/dy)(dx/dz) = -1 Prove that this equation is true. (Hint: Start with a relationship F(x,y,z)= 0 that defines x = f(y,z), y = g(x,z), and z = h(x,y) and differentiate implicitly.)

Derivatives : Related Rates and Rates of Change

1.Water is poured into a conical funnel at a rate of 1 cm3/s. The radius of the top of the funnel is 10 cm and the height of the funnel is 20 cm. Find the rate at which the water level is rising when it is 5 cm from the top of the funnel. I know that I am suppose to use the volume of the cone V=1pi r2h 3 2.A ligh

Derivatives and Rates of Change

1.A ball is thrown directly upward from the ground. Its height above the ground is given by h=50t-5t2 Where h is measured in metres and t is measured in seconds. Determine a)its initial velocity b)the maximum height of the ball c)when the velocity is negative d)how long the ball is in the air e)the velocity with whi

Derivatives and Integrals Initial Voltages

1.) The current in a circuit is i = 2.00 cos 100t. Find the voltage across a 100-microfarad(uF) capacitor after 0.200 s, if the initial voltage is Zero (one microfarad(uF)=10 to the power of -6 F). 2.) Find the volume of the solid of revolution obtained by rotating the region bounded by y = cos x to the power 2, x=0, x = squa