5. Find the appropriate derivatives of the following functions. Complete the calculus steps, but you do not need to simplify your answers. ds (a) The position of an object is given by s(t) = -4.9t² - 3.4t + 8. Find dt (b) In the space below, compute the derivative of two of the following functions. In(x) + x2 e2x – 3x2 F(x) = G(x) = (x-6 – In(x))e-, H(x) = (1+2x² + 3e*)4 6.

Q: 2. Calculate the derivative of the following y= (*- 3 + Sx) B. Ytan (x+ Se-2) (4x + 3) Tx-2) A. C.…

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Q: 1 dt. o t4 +5 Let f(x) = Find the derivative f'(x). e2x none of the choices et

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Q: 1. a) Find the successive derivatives of the following functions: (x' +80x²)* ii) Z (x* +10x +20) 21…

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Q: 4. Find the second derivative for the following functions : a) y=(x+!)' (ans.:6x +6+ 12) x' b)…

A: (a)

Q: Find derivatives of the following functions: y= (4x + 3)/In[2x* +3x -s] y= 3(e" +e*Xx² - 4)

A: ANSWER :

Q: Find the second derivative of the function y=x(x² – 1)² A) None of the given choices B) 2x(5x2 - 6)…

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Q: Find the derivative of the following with respect to the given variable 1. 2x -6x + 15x - 18 2. 5y -…

A: Solution: The objective is to find the derivative of the given functions

Q: 2. Find the derivative of f (t) = (1²-3)° and simplify your answer as much as possible.

A: We have, f(t)=t2+3(t2-3)2   If we f(x)g(x) form, then the derivative of the function will be,…

Q: Calculate the second and the third derivative of y =ar y" -(8/(pix^5)) -(48/(nix^7))

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Q: 1 dt. o t4 +5 Let f(x) = Find the derivative f'(x). none of the choices ex e2x

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Q: Find the derivative of f(x) = In(e +4) 1 O 3e? e+4 3e3

A: We use the chain rule

Q: 2. Calculate the derivative of the following. y = (x*- 3x2+5x) 3 y = tan (x2 + 5x - 2) А. B. (4x +…

A: Given  A. y=(x4-3x2+5x)3 B. y=tan2(x2+5x-2)C. y=(4x+3)3(x-2)2D. y=x2ex2-1

Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

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Q: 1. Find the derivatives of each of these functions: a. y = ln (4x² + 4) b. y = 22² c. y = 25x+7…

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Q: 1. Determine the derivatives of the following functions (a) y = (x² - 2)²

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. D, (x') 2. D, (5x) 3. D. (x-2x)

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Q: c) h(x) =(5x-1) 12x² – 6 d) m(x) = (4x² – 9x} %3D

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Q: 4- Calculate the second derivative of the function y = f (x) defined by the equation x'+y° +3xy +…

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Q: 20. Find the derivative of the function. y = 9cos(2x) a. y'=-18sin(2x) b. y' =18sin(2x) c.…

A: Option (a) is the correct option. Differentiate y using the chain rule.…

Q: 1. Find the derivative of the functions, do NOT simplify. a. y = In(8 – 3x) | b. y = ln /2.x + 1 3a2…

A: We have to pick the most challenging formula among differential formulas and solve it.

Q: Find the first derivative of the following implicit function. x3 + y3 + 3 xy2 = 8

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Q: Calculate the derivative of the following function. 4x y = e **(4x- 1)9

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Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

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Q: If x=t^2 +1 and y= t^3, then the second derivative is * 3 (4t)

A:

Q: 4- Calculate the second derivative of the function y = f(x) defined by the equation x³ + y3 +3xy +…

A: The given function is: x3+y3+3xy+3y2+6x+6y=0

Q: B. Find the first and second derivatives of the following: 1. m(x) = 2(x)(√x) 2. a(x) = √3x 3. [u(x)…

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Q: 27. The first derivative of y = is (4x+1) -24 b. 24 C. -6 6. (4x + 1)+ (4x + 1)+ (4x + 1)4 (4x + 1)*…

A: y=-2(4x+1)3

Q: Use the theorem of Leibniz in the following problems: 1. Obtain the n'th derivative of: x2y [x?y") +…

A: The objective of the question is determine the nth derivative of the given equation.

Q: 5 What is the derivative of5a2 + 10x + ? A None of the given choices B 10x + 10 + 3x2 10a4 + 10a³ –…

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Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y-x) = 9 at x = 1. dy x-x B)…

A: Equation of tangent line is - y- y1 = m(x-x1)

Q: 4. Find the second derivative for the following function a) )* 22 y3(x+ (an b) f(x)=/2x + at x= 2 c)…

A: See the attachment

Q: FIND THE SECOND DERIVATIVE (y") OF THE FOLLOWING IN ITS SIMPLIFIED FORM (COMPLETE SOLUTION): 2 X = 2…

A: First, evaluate the first derivative dydx (y'). To find y', determine the dxdt and dydt.…

Q: 1. Find the first derivative of the following functions: y = f(x) = -(2x + x³)-2 + 4x (2x+4)² (a)…

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Q: 11. Find the derivative of the following function. y=2-6e a y'=54r°e b. y' = -54x°e- c. y' = 6e d.…

A: Given function is

Q: 11 8 Find the derivative of the function: y = 3(x – 4)' x-4

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: 1. [5.1] Determine the equation of a line tangent to the curve of x = 1. f(x) = 5e* +1 at 2. [5.1]…

A: A detailed solution is given below

Q: Find the derivative of y= (x³-1) /(x-1). O a. 2x -1 O b. 2x -3 O c. 2x + 3 O d. 2x + 1

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Q: 2. Find the derivatives of the following functions as specified: a. h (2) = (9z +4), b. g (x) = (æ²…

A: I am attaching image so that you understand each and every step.

Q: Q2: A) Find an equation of the line tangent to the function of x2 + (y- x)² = 9 at x = 1. dy if y =…

A: Derivative of function

Q: Find the derivatives of the functions y = (1 - t) (1 + t2)-1

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Q: 6. 7. 8. Determine the derivative of the curve with equation y = 4²x a) 4²x ln4 b) 42x In2 c) 4* In2…

A: We have to find out derivative

Q: 25. Find the derivative of the function. y = (1+ 3x)e - 3x O A. - 9e - 3x 3x В. - 3(1 + 3х)е - 3x -…

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Q: 11. 5 4 Determine the derivative of y=x° – x* + 6. - Enter your next step here dy ab a + JT 00 () dx…

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Q: 1. Find the derivative of the following by using the Theorem. a. y = In(3x3 – 6x +9) b. y = In[(2x –…

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Q: 3. Find the derivative of y = | (12 +1) dt.

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Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: Find the derivative of the following:  R = (q^2 + 1)^4 y = ln(5t + 1)

A: We have to find derivative of given different functions ,Given different functions are

Q: 18. Up to what derivative is the derivative of y = x6 + 2x5 - 4x4 + 7x³ becomes 0.? a. yv b. yu c.…

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