Find the derivative of the function. f'(x) = = f(x) = 8 √x 16x5 5 + 1

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A: We will derivative the function twice with respect to x and than y and than z as follows.

Q: en h(x)= x³f(x) g² (x) XT) and f(1) = 1, f'(1) = -1,g'(-1) = 3,g(-1) = -2, find h'(- 1²0100

A: Topic:- function and its derivatives

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Q: Determine whether the planes are parallel or identical. -7x + 2y - 9z = 7 21x 6y + 27z = 20 The…

A: The given planes are: P1:   -7x+2y-9z=7           and          P2:   21x-6y+27z=20

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A: Given ex+ydx+2+x+yeydy=0 and y0=1

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A: Topic:- differential equations

Q: In each of Exercises , sketch the shifted exponential curves.7. y = 2^x - 1 and y = 2^-x - 18. y =…

A: Given exponential expressions, 7) y=2x-1 and y=2-x-1 8) y=3x+2 and y=3-x+2

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Q: Which function shows f(x) decreasing as a approaches negative and positive infinity? Select all that…

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Q: Find the tangent equation to the a function x²+4y²-8=0 which is parallel to x-2y=-8. x-2y + 8 = 0…

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Q: K How long will it take money to triple if it is invested at 8% compounded semiannually? 7.4%…

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A: To solve the integral. As per our guidelines we are supposed to answer?️ only one question. Kindly…

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Q: Given that Vƒ(2, −11) = 6 i – 3j, find the directional derivative of the function ƒ at the point…

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Q: Problem 1. Is the following true or false? Justify your choice. 4x (x − 1)(x + 3)' Bx + C x + 3 To…

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Q: a. Graph the function ƒ(x) = sqrt(1 - x2), 0<= x <= 1. What symmetry does the graph have?b.…

A: The given function is: f(x)=1-x2,0≤x≤1. It is required to find the symmetry of graph.

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Q: Solve the ff. Linear Equation: b. (x² + y² + 1)dx + x(x - 2y)dy = 0

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Q: Indicate the degree and determine the solution of the following equations. Homogeneous DE 1. 2(2x²…

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Q: Determine whether the set W is a subspace of R³ with the standard operations w = {(a, -a,0): a is a…

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Q: Determine the domain and range of the following parabola. f(x) = -3x²-24x - 54 Select the correct…

A: Given equation of parabola f(x)=-3x2-24x-54

Q: Consider the following. y² – x² = 384; (8, 8√√7) Find the slope m of the line tangent to the graph…

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Q: 4. (x + y)dy - (2x - y + 3) dx = 0

A: The differential equation Mdx+Ndy=0 is said to be exact if ∂M∂y=∂N∂x. The solution of the…

Q: 4. (x + y)dy - (2x - y + 3) dx = 0

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Q: find y' if y 43 -2 = 2 2m² +5c8cm) (3 cotm-m² 3Гm + cosm

A: We use  Power rule ddxxn=nxn-1 ddxcscx=-cscxcotxddxcotx=-csc2x

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Q: y-values 6 8 7 6 5 4 32 1 If f(x) = f'(1) = g(x) h(x) ' g(x) 2 3 x-values then 4 Out y-values S 4 3…

A: To find the derivative of f(x) at x=1.

Q: 1. Let y=f(x)=x² 4x + 1 (a) Use the definition of the derivative to find the derivative f'(x). No…

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Q: Which of the following is not a differential equation A. dr dy B. (2x+y) dg + 5 =0 cởi treo Dyxdx ao…

A: We need to choose correct option.

Q: DIRECTIONS. Indicate the degree and determine the solution of the following equations. 1. 2(2x² +…

A: NOTE: Refresh your page if you can't see any equations. . the degree is the power to which the…

Q: A national census bureau predicts that a certain population will increase from 31.7 million in 2000…

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Q: se the suggested substitution to write the expression as a trigonometric expression. Simplify your…

A: Given expression:- x2-16

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Q: 3. y У = = e3x-e-3x e3x+e-3x

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Q: 6. For i = √-1, what is the sum (7 + 3i) + (−8+9i)? (A) -1 + 12i (B)-1-6i (C) 15 + 12i (D) 15 - 6i

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Q: PLOT THE GRAPH FOR THE GIVEN CURVES AND CONDITIONS BELOW Need to find out the differential equation…

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Q: 3. Multiply: (-2-7)(-2+71)

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Q: For the function f(x) = -6x²-3x + 3, evaluate and fully simplify each of the following. f(x + h) =…

A: Topic-Functions We are given , f(x)=-6x2-3x+3 and we know that (a+b)2=a2+b2+2ab

Q: Why did you subtract 115-105 in question #2 and not 110-105? Where did 115 come from?

A: Note:  After seeing the previous solution, we observe that the expert has provided the wrong…

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Q: Find a parametrization of the parabola x = y². Don't forget an interval for the parameter. (Hint:…

A: Please see the below picture for detailed solution.

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Q: What is a periodic function? Give examples. What are the periodsof the six basic trigonometric…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A: Given lines are L1: x=2-t ,  y=3+5t, z=4+3tL2: x=4t, y=1-20t, z=4-12t

Q: Using the Second Derivative Test, find the relative extrema and saddle point(s) of f(x, y) = 2x³ +…

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Q: In Exercises 57-64, solve for t. 57. a. e0.3t = 27 b. e = c. In02 = 0,4 %3D 58. a. 0.0l = 1000 b. c.…

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

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Let's find directional derivative.