Find f'(x) and simplify. f(x) = 8x*(x³ -9) 3 Which of the following shows the correct application of the product rule? O A. (8x) (3x²) - (x³ - 9) (32x³) 3 OB. (8x) (3x²) + (x³ - 9) (32x³) 3 OC. (8x) (32x³) + (x³ - 9) (3x²) OD. (3x²) (32x³)

Q: Suppose f (x, y, z)= + P = (2, 4, 3). A. Find the gradient of f.

A:

Q: Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal…

A: Solve triangle ABC .  Whose sides are a= 14 , b=15 and c= 26 .  Find Angles A, Angle B and Angle C.

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. -√³x 5 y…

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A:

Q: Frequency A 1 5 Class width= 9 Based on the histogram above, what is the class width? 13 17 21 25…

A:

Q: Determine the periodic payments PMT on the given loan or mortgage. (Round your answer to the nearest…

A: A=P(i[1+i]n)[1+i]n-1where A is the periodic payment amountP is the principali is the periodic…

Q: f(x) = ln(x), ro= 100, and 2₁ = 105.

A:

Q: In calculus, this expression is called the difference quotient of f.(a) Express the slope of the…

A: Note:- Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Q: Determine the equation of the plane containing the point and the line. (-7, 10,-3), r(t) = (1 - 4t,…

A:

Q: dy What is the IF for solving the linear equation: x dx O A. O O m L O O O E. X2 3x 2 MIN -Lnx 2 3x…

A: It is a linear differential equation

Q: Find the limit, if it exists, or type N if it does not exist. 2x² lim (x,y) (0,0) 4x2 + 1y²

A:

Q: Two ships leave the same port at noon (12PM). Ship A sails north at 15 mph, and Ship B sails east at…

A:

Q: 1. Given the vectors a³ = (2, −1, 3), b` = PQ` where P(1, 1, 1) and Q(5, 1, −1) and c³ = i̇ + j³ +…

A:

Q: Graph the following equations and explain why they are notgraphs of functions of x.a. |x| + |y |= 1…

A: Given data:- (a);  x+y=1 (b); x+y=1

Q: 4. Linear Equations b. 2y(y² - x)dy = dx

A:

Q: 1. Find the domain of the following functions. Decide if the graph of y = f(x) is even or odd. (a)…

A: Domain: The set of all those values of x such that function f(x) exists at those points.A function…

Q: If 2 = (x + y)e*, x = 3t, y = 4-t², find dz/dt using the chain rule. Assume the variables are…

A:

Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? None…

A: Given (y+1)dx+(4x-y)dy=0 Multiply both sides by 1(y+1)dy (y+1)dx(y+1)dy+(4x-y)dy(y+1)dy=0…

Q: Explain how to use mathematical induction to prove that a statement is true for every positive…

A: Mathematical Induction is a technique for proving certain types of mathematical statements.

Q: Find Vz. = sin(5y² - 5xy) NOTE: Give your answer in unit vector notation; that is, in terms of i and…

A: Topic:- derivatives

Q: the space curve (t) = (2t, t², 2t)

A:

Q: f(a+h)-f(a) h Jse algebra to simplify by hand and then letting h→0 to find f'(a) where: A. f(x) = 5x…

A:

Q: First-class Mail In 2015 the U.S. Postal Service charged$0.98 postage for first-class mail retail…

A: Given that Postal Service charged $0.98 for postage weighing up to 1 ounce, plus $0.22 for each…

Q: e Monday by Question Use the formula 8x7 4+x4 Include +C in your answer. to evaluate Provide your…

A:

Q: -3 Σ Σ 4 Τ 1 Σ k=i (k + 2)(k + 3) IME 1 4*+2 7K-1

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: Factor out the greatest common factor. Simplify the facto 48x^(8)y^(8)-84x^(4)y^(5)+24x^(

A: Topic:- algebra

Q: what is rational function ?

A: Relational number Our connection is number three. As you'll see that number is specific to our…

Q: what is cubic functions ?

A: Function:- A relation between a set of inputs and outputs is known as a function. To put it simply,…

Q: In exercises 87 and 88, use a graphing utility to graph the function. Then, graph  P1(x)=…

A: Given f(x)=ex So, f'(x)=ex So, f"(x)=ex So, P1(x)=e0+xe0=1+x  So, P2(x)=e0+xe0+x²e0/2=1+x+x²/2

Q: is thrown straight down from the top of a 470-foot building with an initial velocity of -23 feet per…

A: Given query is to find the velocity different points.

Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A:

Q: 3. Let x² + 4xy + y² = 13. dy • Find dx by using implicit differentiation.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Give the center, foci, vertices & asymptotes. Sketch the graph y - x = 1 y + x

A:

Q: 5. Bernoulli's Equations b. 2x³y' = y(y² + 3x²)

A:

Q: Goals 12-13-14 In Exercises 1-16, find (a)domain D, (b) holes, (c) vertical asymptotes, (d)…

A: Disclaimer:  “Since you have asked multiple question, we will solve the first question for you. If…

Q: Solve for the value of C in the equation: (3xy² + 2y)dx + (2x²y + x)dy = 0 when y(1) = 2 OA. 4 OB.…

A:

Q: The integrating factor (IF) of the equation y' - 2ycot2x OA sin2x OB. cot2x OC.Lnsin2x OD. CsC2x OE.…

A:

Q: Determine whether the values in each table belong to an exponential function, a logarithmic…

A: Given points, a) A (0,7) B (1,4) C (2,1) D (3,-2) E (4,-5) b) A (0,1) B (1,4) C (2,16) D (3,64) E…

Q: Which of the function is not an exact equation of the first order? OA. (ey + ycosx)dx + (xe³ + sinx…

A: See this solution in below.

Q: 1. Find the differential equation representing all circles with the center on the line y = x and…

A:

Q: find the average rate of change of the function over the given interval or intervals. 5. R(0) = V40…

A: Given expression, Rθ=4θ+1 0,2 a=0 b=2

Q: The degree of homogeneity of the function ƒ(x, y) = (x² − 4y²)−1/² O A. 1 OB. -1 O C. -1/2 O D. None…

A:

Q: Find a and b so that the function is both continuous and differentiable. a= 76 b= 80 Note: You can…

A:

Q: Given that the directional derivative of ƒ at the point (9, –9, 4) in the direction of a = 4 i – 4j…

A: We know that magnitude of a vector is given as-  If V = ai + bj + ck then magnitude is  |V| =…

Q: In Exercises , say whether the function is even, odd, or neither.Give reasons for your answer.51.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: f(x) = -3x² √x²-4

A: Domain is =-2<x<2

Q: Differential equations 2xe²tdt+(1+e²¹)dx=0 exact

A:

Q: Write the equation of the plane with normal vector n = (-6, 4, 2) passing through the point (4, 6,…

A:

Q: What is the value of k so that the differential equation (y³ + kxy4 − 2x)dx + (3xy² + 20x²y³)dy = 0…

A: We need to find out the value of k that makes the given differential equation exact.

Q: (g) Differentiate g(x) = V/1-2²-cos¹ (√2) COS (h) Find (1) Find do [sec (arctan (62))] de sin-¹(cos…

A: