Differentiation Questions and Answers

Consider Determine the derivative of y with respect to x. y' cos(xy) = y³ =

Consider Determine the derivative of y with respect to x. dy dx = xe8 = – 5y

Let h(w) = 4w - 8 log3 (66) Determine the value(s) of w, if any, for which h has a horizontal tangent line. If mulitple such values of w exist, use a comma-separated list to enter the solutions. Oh has a horizontal tangent line at w = Oh has no horizontal tangent lines.

Natasha records the price for a gallon of home-heating oil from 20 randomly selected providers in her region on May 15. She does it again with another 20 randomly selected providers on November 15. The results (in dollars) are shown in the accompanying samples. Each date had one provider that had a price of $2.879 per gallon. Is the $2.879 price per gallon more unusual to occur on May 15 or November 15? Use Excel to calculate the z-scores for a price of $2.879 on May 15 and on November 15, rounding to two decimal places. Provide your answer below: May 15 z-score: November 15 z-score: ✪ Help 15-May 2.849 2.839 2.859 2.699 2.759 2.889 2.789 2.739 2.789 15-Nov 3.069 3.109 2.879 2.959 3.069 3.049 3.089 2.929 2.909 Copy to Clipboard Download CSV Next

Find the derivative of the algebraic function H(x)=(x-5)(x³ +3)

This question asks for an algebraic expression. With these types of questions, be sure to use the variables indicated. In your answer, you can also use mathematical expressions for numerical calculations. Examples with trig functions and logs Type To get sin(pi/3x) In(x)/Ln(7) arcsin(x) sin Enter sin (*) In(x) In (7) arcsin(x) With any function like log, In, sin, etc. be sure to use proper function notation; sin(3) is OK, but sin3 is not. Unless the problem gives specific directions, any algebraically equivalent expression is acceptable. For example, if the answer was log(5x), then log(5) + log(x) would also be acceptable. Try it here. Use the Preview button to see how the computer is interpreting what you typed. In (3) 3 (5₂) + below

A plant can manufacture 50 golf clubs per day at a total daily cost of $4883 and 60 golf clubs per day for a total cost of $5533. (A) Assuming that daily cost and production are linearly related, find the total daily cost, C, of producing x golf clubs. (B) Graph the total daily cost for 0≤x≤ 200. (C) Interpret the slope and y intercept of the cost equation.

Precision Aviation had a profit margin of 6.25%, a total assets turnover of 1.5, and an equity multiplier of 1.8. What was the firm's ROE? O a. 20.93% O b. 16.88% c. 13.84% d. 14.34% e. 17.72%

This question asks for a fraction, a reduced fraction, and a mixed number. 2 Enter fractions like 2/3 for the same as if 1/1/1 15 For a reduced fraction answer, be sure to reduce your fraction to lowest terms. If 2 Enter 2 is not reduced, and would be marked wrong. 4 Enter 1 2 711 171 For both fraction and reduced fraction type problems, improper fractions are OK, like numbers will not be accepted. 3 3 3 . For this type, the fraction does not need to be reduced, so 2²/14 1 +2/7/20 Enter 2- 3 For a mixed number problem, enter your answer like 5 1/3 for 5. Improper fractions will not be accepted. Also, be sure to reduce the fractional portion of the mixed number to lowest terms. Try it here. Use the Preview button to see how the computer is interpreting what you typed. (does not have to be in lowest terms) is the correct answer, (does have to be in lowest terms) 10 is considered -, but mixed 3

Let sine= 2√3 and <0<x 5 2 Part A: Determine the exact value of cos 20. Part B: Determine the exact value of sin O|N

3 = Given g(x) find g' (1). Round your answer to the nearest hundredths (two digits after the decimal). 800 x - 6x

Part 1 of A box with a square base and open top must have a volume of 119164 cm³. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. A(z) = = 3+476656 H Next, find the derivative, A'(x). Part 2 of 4

(1 point) Let F = xi + (x + y) j + (x − y + z) k. Let the line / be (a) Find a point P = (xo, Yo, Zo) where F is parallel to 1. P = Find a point Q = (x₁, №₁, Z₁ ) at which I and I are perpendicular. Q= = 3-t, y = 5t-1, z = 1+ 3t. Give an equation for the set of all points at which I and I are perpendicular. equation:

Use the x-cubed tool to graph the x-cubed function. Update the function to have a Vertical Stretch of 3, a Horizontal Stretch of 1, a Vertical Shift of 0, a Horizontal Shift of 5, and a Reflection over the x-axis.

Solve using matrices: 3x - 2y + 2z = 6 7x - 3y + 2z = -1 2x - 3y + 4z = 0

Use logarithmic differentiation to determined at x =1 for the following function: y=√x+1/(x+2)(x³+1) -7√2/72 7/ 2√2 √2/6 7/12

= . Let u(x, y) be the solution to the boundary value problem uxx + Uyy 0, for all (x, y) such that x² + y² < 1, and u(x, y) = x², for all (x, y) such that x² + y² = 1. Find u(0, 0).

Determine, with motivation, whether the following function satisfies Dirichlet's conditions on the given interval: f(x) = cosec(x) with f(x) = f(x + π) on (-₁) [2]

Find dy/dx by implicit differentiation. √xy = x³y +32 dy/dx =

What are the Cartesian coordinates of the point whose cylindrical coordinates are (r, 0, z) = (4, 2.6, -6) ? (x, y, z) = (

1. Consider the function, f(x) = 6 arctan(x). (a) (4 points) Find f'(x) using any method. f(x)= barctan (x) bask 6 x² +1 (b) (4 points) Compute f(0) and f'(0).

Find dy/dx by implicit differentiation. 6x²y +9y²x = -6 dy/dx =

Find for the following: y = ln (2) dy da e² (In 2) Oe²x 02

Find dy for the following: da xy - In(xy) = 1 O 0 - 12/10 x Y O Ake O- - I Y

Consider the following. x² + y² = 9 (a) Find two explicit functions by solving the equation for y in terms of x. (positive function) Y1 = Y2 = (negative function)

Perform the indicated operations (2x^2-6x+11)+(-3x^2+7x-2) (-4y^2 - 3y+8)-(2y2-6y - 2) 6x(-2x^2+5x+6) (9k+q)(2k-q) 5. (2m+1)(4m^2-2m + 1) All up arrows are to the 2nd power

Find dy/dx by implicit differentiation. cot(y) = 8x - 4y

The loudness L(x), measured in decibels, of a sound of intensity x, measured in watts per square meter, is defined as L(x) = 10 log can detect. Determine the loudness, in decibels, of a sound with intensity of x = 10-10.8 watt per square meter. where lo = 10 - 12 watt per square meter is the least intense sound that a human ear

Find the vertices, foci, equation of the asymptotes, transverse and conjugate axis length for 9y² - 25x²= 225. Type the equation in standard form and then state the five answers. Checklist: 1) State equation in standard form (2) State the vertices 3) State the foci 4) State the equation of the asymptotes 5) Give the length of the transverse axis 6) Give the length of the conjugate axis

The Louvre museum in Paris features an inverted square pyramid with a height of 10 m. The side of the square is 13 m. Super-villains decide to fill the pyramid with water, and do so at a rate of 10 m³ per second. How quickly is the water level rising when it reaches the top? (10 marks)

If you make $2500 in Gross Income every month, but 35% is taken out in taxes, what will your monthly Net Income paycheck be? O $1500 $875 $2500 $1625

1. Match the Vocabulary word with the definition below. (18 pts.) f h 9 e b d C a Y 1. FICA tax ▾ 2. Withholding V 3. Tax Revenue 4 4. Income Tax V 5. Internal Revenue Service 6. Property Taxes 7. Taxes 8. Medicare 9. Payroll Taxes a. FICA tax, Medicare tax, federal income tax, state income tax, and other local taxes are all part of a specific tax. b. The federal bureau that is in charge of collecting income tax and processing tax returns. c. Government income that they get from taxes. d. Payments to governments that are then used for public goods and services. e. A certain percentage is taken out of your income and is used to fund this program. f. Taxes that you pay based on your salary, hourly wage, tips, or interest. g. This is money that is withheld from your paycheck by your employer and given to the government to use. h. "Federal Insurance Contribution Act" that funds social security and Medicare. i. You pay these taxes if you own a home, boat, car, ATV, etc.

5. Enter your response into the blank field using one word only. income is the total amount of what you earned. (2 pts.)

3. Banks will pay you interest on your money based on the interest rate. (4 pts.) O True False

Match the financial institution with its definition. (6 pts.) V ▼ 1. Credit Union 2. Bank 3. Brokerage Firm a. A business where stocks, bonds or mutual funds are sold. The can be found in your hometown or on the internet. b. An organization chartered by either the state where it is headquartered or by the federal government. c. A non-profit company that is owned by its stockholders and provides checking accounts and other financial services.

Complete the table to find the derivative of the function. Original Function Rewrite 7 y = Differentiate Simplify

Use the Product Rule to differentiate the function. f(x) = x cos(x) Step 1 To use the product rule, write the given function as the product of two functions. f(x) = g(x)h(x), where g(x) = x and h(x) Step 2 The product rule states that (g(x)h(x))' = g(x)h'(x) + g'(x)h(x). Find the derivative of g(x). g'(x) = 6x5 Find the derivative of h(x). h'(x) = sin(x) 6x5 - sin r = = cos(x Step 3 Substitute for g(x), g'(x), h(x) and h'(x) to find the derivative of f(x). f'(x) = x( (6x5) ) + H

Suppose f'(5) = 8 and g (5) = 9. Find h'(5) where h(x) = 4f(x) + 2g(x) +2.

Find the maximum and minimum values of the function and the values of x and y where they occur. F = 5x +36y, subject to 6x + 4y ≤ 35, 4x+6y ≤ 30, x ≥ 0, ≥ 0. y M What is the maximum value the function? (Simplify your answer.) Where does the maximum value occur? 7 (Simplify your answer. Type an ordered pair.) What is the minimum value of the function? (Simplify your answer.) Where does the minimum value occur? 1 (Simplify your answer. Type an ordered pair.)

Use the given function f to answer parts (a) through (f) below. X f(x) = 4 +5 T A. The horizontal asymptote of f is y = 5. (Simplify your answer.) OB. There is no horizontal asymptote. (d) Find f1, the inverse of f. f(x)= (Simplify your answer.) G (c) From the graph, determine the range and any asymptotes of f. The range of f is (5,00). (Type your answer in interval notation.) Determine the horizontal asymptote of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

nt) A boat is heading due east at 21 km/hr (relative to the water). The current is moving toward the southwest at 9 7 . Give the vector representing the actual movement of the boat. 20.23 deg How fast is the boat moving, relative to the ground? km/hr. By what angle does the current push the boat off its due east course? Your answer should be a positive angle less than radians.

Find the numerical derivative using NDER on your calculator. f(x)=1-x-2x^2 at x = 2

Find the differential of the function. y=(7-t^6)^-2 dy=_____

Find the differential of the function. y = (8+COS(θ))^-2 .dy =

Use the definition of a derivative, lim f(x+h)-f(x)/h to find the h→0 derivative of the following function: f(x)=x²-3x

A street light is mounted at the top of a 15-ft-tall pole. A man 6 feet tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast (in ft/s) is the tip of his shadow moving when he is 40 feet from the pole?

If x^2 + y^2 + z^2 = 9, (dx/dy) = 3, and (dy/dt)= 9, find (dt/dz) when (x, y, z) = (2, 2, 1). dz/dt =

How do you find f(b), if you are given f(a), and f'(t)?

If you are given the rate of change of a function f, and an interval, what is the total change over the interval?

If f'(x) < 0 for x < -2 and f'(x) > 0 for x > -2, then it can be concluded that f has a relative minimum at x = -2. A) True, the derivative changes from positive to negative. B) True, the derivative changes from negative to positive. C) False, the derivative changes from positive to negative. D) False, the derivative changes from negative to positive.