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Q: x2-1 7) lím x--1 x+1 (x+4)ln(x+6) 8) lím x--4 9) lím x-0 Vx+5-V5 x2-16

A: Compute the limit as follows. limx→-1x2-1x+1=limx→-1x2-12x+1=limx→-1x+1x-1x+1…

Q: (x + 2)8(4x – 1) (6x + 6)2 Let f (x) = %3D Use logarithmic differentiation to find the derivative of…

A: SOLUTION-

Q: 8. f(x) = (2(3x+1)(3)) (4x – 1) – (3x +1)²(4) (4x – 1)2 Note: This is the form that the first…

A: We have Fx=23x+134x−1−3x+1244x−12Fx=36x2−18x−104x−12

Q: 1. Find the derivative of the expanded function a. a^2x^2+2abx+b^2 b.…

A: 1. a) Given, a2x2+2abx+b2 Consider, y=a2x2+2abx+b2 Differentiate with respect to x,…

Q: 5V3 6. Question 9 Find the derivative of (8 x + 1)*. a) O (8 x + 1)* (3 In(8x + 1) – - 8x + 1) b) O…

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Q: Match the functions in Column A with their derivatives in Column B. 1. f(x) = 4 А. f'(x) = 8x 2.…

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Q: 20. The fourth derivative of y = Jx -1 is 5 3 A. (x - 1) 8 15 В.- (x-1) 16 3 C. - (x- 1) 3 8 8 D. -…

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

Q: The first derivative of the given function is y = In(1 – 2x)³(2x + 1)? 10x+1 2x+2 1-4x2 1-4x2 20x+2…

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Q: A) Differentiate y = 4√x + 8 / x - 6 / 3√x +10 B) Find the second derivative of y = 4 √x + 8/x - 6…

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Q: Use logarithmic differentiation

A: Taking natural log on both sides,

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Q: Find the derivative of: h(x) = (3x-2)/(x^2+2) 3/(2x) (-3x^2+ 4x + 6)/(x^2+2)^2 (-3x^2- 4x +…

A: The solution are next step

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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

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Q: Question (3) Estimate the first and second derivatives of f(x) =-0.1x 4 - 0.15x 3 - 0.5x 2-0.25x+…

A: Solution:Estimate the firts and second derivative of fx=-0.1x4-0.15x3-0.5x2-0.25x+1.2at x=0.5 and…

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Q: 9x Find the derivative of the function f(x)=In x2+15 2x O f'(x)= x²+15 15-x2 f"(x)= x2+15 2x O…

A: Click to see the answer

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Q: Find the derivative of the function. x2 +5 g(x) = x2 + 6x 6х? - 10х - 30 O A. g'(x) = x²(x + 6)2 2x3…

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

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Q: 3 (x2-18x) x - 36 Use logarithmic differentiation to find the derivative of y 1.

A: Given , y=x2-18x3x2-364

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Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

A: Click to see the answer

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Q: Find the first derivative: y = In V2x3-5 Oý = 203-5 O y = 4x2 203-5 3x2 O Ý = 23-5 O Ý = 6 52 y =…

A: Click to see the answer

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Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

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Q: The first derivative of f(x) = e5x*-6x will be A. (6-20x)e**-6x B. (20x 6) e5x*-6x C. (6+ 20x)…

A: Click to see the answer

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Q: Consider the function g(x) =2x³ - 6x+3. The critical values for this function are and since these…

A: We have to find critical points

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Q: 3x+7x What is the first derivative of f(x) = In(A? 5x Select the correct answer below: Os) = 6x-7…

A: Topic:differentiation

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Q: (x + 4)7(3x – 1) (7x + 5)3 - 4 Let f (x) Use logarithmic differentiation to find the derivative of…

A: Click to see the answer

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Q: Find the derivative of this complex equation using logarithmic differentiation?

A: Click to see the answer

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Q: Find the derivative of each function. 1. f(x) = 3x* +5x-2 2. g(x)=-4x+5x'-2r+3 3. f(1) = 25+7NP - 4.…

A: Click to see the answer

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Q: .4 In(12x + x), the derivative Given g(x) = g (x) is 12x4 + x 48x3 + 1 48x +1 12x4 + x 4x3 48x³ + 1

A: Given, gx = ln12x4+x We have to find the derivative g'x .

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Q: Find the derivative of: h(x) = (1/x^2 - 1) / (1/x -1) (1/x -1)^2 –1/x^2 (1/x^2 – 1)^2 (1/x +1)^2…

A: Click to see the answer

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Q: Find y’ when y^2 e^2x = 3y + x^2 and y(0) = 3 a. -5 b. -7 c. -6 d. -4 e. -2 f. -1 2. Find the…

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Q: 7. Find the derivative of each funcrion. a. y = 5-4* b. fCx) = xqx d. FCx) = Togax-1 C. Y =…

A: Click to see the answer

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Q: If f (x) = x* and g(x) = x³, then f'(x) = 4x³ and g'(x) = 3x². The Chain Rule %3| multiplies…

A: It is given fx=x4, gx=x3, f'(x)=4x3 and g'(x)=3x2.

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Q: What is the second derivative of In(x4– 1)? - 16x9+ 12x6– 12x² (A) (x4– 1) 2 4x3 In (B) - 4x6– 12x2…

A: Click to see the answer

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Q: Question 19 What is the derivative of 1 1 y = 2x + 3x 2 + 2 ? - - 2 Y = 2x 3 4x 5 5x 2 3 2 y = 12x 5…

A: Click to see the answer

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Q: Find the derivative. 8) y = (x + 1)2(x2 + 1)-3 A) - = 2(x+ 1)(x2 + 1)-4(2x2 - 3x - 1) B) Y =-2(x +…

A: Click to see the answer

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Using the product rule of natural logarithm, it can be written that ln(ab)=ln(a)+ln(b) . Using the…

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Q: Find the first derivative for the following function. Vx4 – 3 (2х — 5)"] f(x) = ln (2x-5)7 Vx4-3 2x3…

A: Click to see the answer

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Q: Find the derivative of the function. y = (3x + 1)°(x+ - 6)° A y=(32x +9)(3x +1) (x*-6)° B y' = 9(3x…

A: Click to see the answer

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Q: 1. Find ALL THE DERIVATIVES of the function: f (x) = 2x7 – a5 + 5a³ – 8x + 4 2. Use logarithmic…

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Q: 3x +2x-4 derivative of the function of ƒ(x)= %3D 7x² -9x+2

A: f'(x) = (- 41x² + 68x - 32)/(7x² - 9x + 2)² The detailed solution is as follows below:

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Q: Find the derivative of: g(x) = (1+1/x) / (1 – 1/x) -2(x-1)^2 (1+1/x) (1-1/x) / (1 – 1/x)^2 (1 –…

A: Click to see the answer

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Q: 8. Find the third derivative of each function. 8.1. h(x) = 5x3 – 2x² + 10 x – 15 8.2. k(x) = e2× +3…

A: The given function is hx=5x3-2x2+10x-15

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Q: Find y' by in differentiation 1.) y= (x^2 + 1)^4 (x^3-10)^5 2.) y= 6x^2 (x+5)^3 / (2-x)^2

A: (1) ddxx2+14x3-105 Apply the product rule: f·g'=f'·g+f·g' f=x2+14, g=x3-105…

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Q: Find the derivative of the given function 4. g(x) = (4 – 9x²)3 5. h(x) x+5 = x2-9, 6. A(x) = v3x3 +…

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Q: FIND THE DERIVATIVE OF THE FUNCTION DESCRIBED. (25 1. y (x2- 1) (2x+1) 2. y 2x2 (4x² + 3x- 5) 3 y +1…

A: Click to see the answer

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Q: (x + 8)®(3x – 1) (6x + 6)4 Let f (x) = Use logarithmic differentiation to find the derivative of f.…

A: Click to see the answer

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Q: 5.2 Compute the derivative f'(x) of the logistic sigmoid 1 f (x) = 1+ exp(-x)

A: Click to see the answer

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Q: 4. Use logarithmic differentiation to find a formula for f'(x): (x+ 1)3/2(x – 4)5/2 (5x + 3)2/3 |…

A: Click to see the answer

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Q: Question 18 Evaluate the first derivative of the implicit function: 4x2 + 2xy +y = 0 4x +y A X+y 4x…

A: Click to see the answer

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Q: If 5x2+2x+xy=45x2+2x+xy=4 and y(4)=−21y(4)=-21, find y'(4) by implicit differentiation.

A: We have given the function

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Q: Find the general form of the function whose second derivative is 2 . 8 x 5/2 + C 1X (A 15 8. x 5/2 +…

A: Click to see the answer

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Q: An observation indicates that the frog population Q(t) in a small pond is 25 initially and satisfies…

A: Click to see the answer