(Inverse Trigo, Higher Order Derivative, Chain Rule) Directions: Find the derivative of the following functions. 1. f(x) = (2x³ - x²)³ (3x5 +4x²)² 2. g(x)= tan-¹ 4x³ 5x+√x 3.y= (x²+1)² 4. Using y = 5x + 3x² + 1, find all the derivatives and evaluate f"(2) and f(3) (-2). 3x4 5. Find the first three derivatives of the function h(x) = ³² + 4x³−²+7

Q: 3. A rectangular plate is submerged in water as shown below. The top of the blue region is the…

A: Given

Q: W=-Si ; V=1-2i, W=-3-6i , U-3V+ 2W, UV, UVW, : Given U= 4-2i ; V= 3-4i atib= (utiv)w, find a ad b.…

A: Here is the solution:

Q: evaluate * √2 2 dw √11+10w-w² O = -0.7973 O=-11.574 = -0.7297 One Hand on Pen, Other on Phone, One…

A:

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

A:

Q: The integral can be rewritten as 6u³ (a). u + 1 6u4 (c). u² + 1 :). -du du dx 3³√x + √√x 派 派 6u² u²…

A:

Q: Find the volume of the parallelepiped determined by the vectors (0, 4, −5), (2, 0, 5), and (-1,3,0).…

A:

Q: The region is bounded by y = x³, y = 2x + 4 and y = -1. Then Arearegion = [*^f(x) dx + [²8(x) x +…

A:

Q: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

A:

Q: f sin 3x cos 5x dx ¹29 sin 3x cos 5x + cos 3xsin 5x + C 16 sin 5xcos 5x + C O. 16 sin 3x cos 3x + O…

A:

Q: iven that x = sin-¹-3). what is the exact value of cos(x) A 10 3 √10 B 3 2√2 3 Ⓒ ²√² D

A: Given query is to find the value of cos x.

Q: Evaluate (2a³y +9y³)dA, D is the region bounded by y 33522 a. 5 Ob. 4811 5 C. None of the choices.…

A:

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

A:

Q: x^2 - 5x + 8 is equal to • 4(2x-5)^2+7 O 2(x - 5)^2-6 O (x-5)^2-9 none of the choices टट

A:

Q: In the partial fraction decomposition for some numbers A, B, and C. Find the value of B? -x²-x+2 C A…

A: On solving this we will get:  B= 1/2

Q: x-y •SS=20₁ -dA over a square region Using the transformations u=x-y and v=x+y to evaluate xx+y with…

A:

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 4x + 8y = 8,…

A:

Q: Which of the following integrals represents the area enclosed by the smaller loop of the graph of r…

A:

Q: Answer and give the complete solution. A 6-ft tall man is walking away from a 15-ft post at a rate…

A:

Q: Given; S √ √ tex. dx 2 Applying rationalizing substitution, find dx in terms o 2 z dz A z²+2 z dz B…

A: Given query is to find dx in terms of z.

Q: Which of the following is TRUE about the given in Example 2 of the video below? Derivative of…

A:

Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).

A: We have to find dy/dx.

Q: For any real x, what is the maximum value of the expression y = 2(k-x)(x+√x²+k²)?

A: This question can be solved using the concept of maximum and minimum.

Q: Question 8 The value of x for which the series Σ QAX<2 or 4<x. OB2<x<3 or 3 <x ≤ 4. OC. None of the…

A:

Q: A light is placed on the ground 30 ft from a building. A man 6 ft tall walks from the light toward…

A: This question is based on application of derivative.

Q: Illustrate the angle 5π Answer in 20mins

A:

Q: Using S- dx x√√x-1 Rationalizing Sfy)dy, find ffy)dy Substitution

A:

Q: What is the area of the region enclosed by the graph of r² = 3 + cos 0? √ √3+ cos e de √(3 + cos 0)…

A: We have to choose correct option.

Q: Suppose that the price-demand and the price-supply equations are given respectively by the…

A: The price-demand equation is p=Dx=40-0.2x and the price-supply equation is p=Sx=27.5+0.001x2. (a)…

Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

A:

Q: 3. f(x) = x² + 1 and g(x) = -x² +10

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: (a) Evaluate the following integrals: π cos(x) dx dy 4y

A:

Q: Use the shell method to find the volume of the solids generated by revolving the shaded region about…

A: Volume of solid revolving about x axis  between curves h(x) and f(x) is given by

Q: X 4e -aluate of v dx 2 se rationalizing substitution. 8

A: solution is given below

Q: Let R be the region bounded by the functions f(x) = -2x² - 7 and g(x) = -9 as shown in the diagram…

A:

Q: 2. Consider the spherical equation given by p = 4 cos 0 sino. Determine its corre- sponding equation…

A:

Q: What is the corresponding Cartesian coordinates for the polar point (-4,-)? (2√3,-2) (-2√3,-2) O…

A:

Q: Let L(r) be the linearization of f(x) = sin x + 1 at the point x = . Find L(π/2).

A:

Q: create 2 sample word problems of chain rule of differentiation  with solutions

A: Solution:

Q: Use polynomial long division to write 2x² + x³ 3x² + 4x-9 - = Q(x) + 1²+1 = p(x) 1²+1

A: To divide using the long division.

Q: Answer and give a complete solution. A ladder 25 ft long stands against a wall. The lower end is…

A:

Q: A manufacturer is planning to sell a total of 500 machines to both foreign and domestic firms. The…

A: Let's find revenue function.

Q: Evaluate the following double integral over the given region R. 4 ln(y + [[ (x+1)(y+1) dA over the…

A:

Q: 3. Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: given isr=2-3cosθ

Q: 5. The region is bounded by y = x³, y = 2x + 4 and y = -1. Then, Area region = [*f(x) dx + [[g(x)…

A:

Q: 1- f(t) = 2t³; 3–f(t)=sinh(2t); 5-cosh (t) sin(2t);

A: Given :1. f(t)=2t33. f(t)=sinh(2t)5. cosh(t).sin(2t)

Q: Evaluate the limit using L'Hopital's rule. Answer should be expressed as an INTEGER value, with NO…

A:

Q: find 04 O B O 7 O -12 af ду dy' given f (x, y) = e + 2xy² – 4y at (0, 3) -

A:

Q: Find O does not exist O-1/2 00 01 D 01/2 O Other e-1-1

A: We have to find the limit

Q: The area in the first quadrant bounded by y = x², the circle x² + y² = 2, and the x-axis π b is…

A: Area

Q: Evaluate the following double integral over the given region R. 11 2 ln(x + 1) (x+1)y Use…

A: