A. Determine the derivative of the following using the Four-Step Rule. 1. f (x) = 4x – 5 2. f (x) = 3x² + 6x – 5 Determine the derivative of the following using fundamental rules of differentiation 1. f (x) = 9x³ – 3x² + 2x – 6 - 2. f (x) = (8a² – 6) (5æ + 4)

Q: 1) Find the second derivative for the following functions: a) f(x) = 4x³ + 3x² + x – 14 b) f(x) =…

A: Solve derivative a fx=4x3+3x2+x-14b fx=4x-3+2x-4c fx=5ex-e3x

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: 5) Find the derivative of each of the following functions. a) f(x) = (3x- 6x - 7) %3D b) g(t) = V4t-…

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Q: Find the first derivative of y with respect to x (y') of the given function using rules for…

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Q: 6. Find the derivative for each function, and simplify (reasonably): a) j(x) = (3x² + 3x – 1)* b)…

A: According to the chain rule of differentiation:   According to the Product rule of differentiation:

Q: 2. Find the derivative of the following functions. (a). g(x) = cos (2x + 1) (b)," f(x) = In (x² – 4)…

A: To find the derivative of the functions

Q: 1. Find the derivative using chain rule. (a) f(x) = (x5 – 2)20 %3D Answer: (b) f(x) = V3r² + 1 %3D…

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

Q: 18 The derivative of the function f(x) = x² + is 18 4x3 + (æ³) 18 O 4x³ - (æ²) 18 4x° + (x) 4x + 18…

A: d/dx(xn)=nxn-1 Given f(x)=x4+18/x  To find the derivative of f(x) differentiate once

Q: 1. Determine the first derivative of the functions below with the rules for deriving the function:…

A: A Given function is y=4x3+32. Use formula ddxxn=nxn−1 Differentiate  y=4x3+32 by using the chain…

Q: Find the derivative of the following using First Principle. 4) y = -2x2 + 3x – 12 5) f(x) = x2 + 15x…

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Q: Find the derivative of the following: 1. y=x(V1- x³ ) 1+x 2. у-. 1-x (x³+5) V4-x² 3. у — x*-x2+6 sin…

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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: Find the derivative of:  a. 1/x^3 + 3 1/ square root of x b. x^3+2x over x^2+3x+ pi^2 c.…

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

Q: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

A: Given query is to find the derivative of the expression.

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

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

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Q: A. Determine the derivative of the following using the Four-Step Rule 1. f (2) — 5а — 4 %3D | 2. f…

A: Recall: Derivative using Four step Rule:step 1 : Write f(x+h) and f(x).step 2 : Compute f(x+h)-f(x)…

Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In x² + y²

A: Given,            f(x, y)=3xy2+2xy+x2ln1x2+y2

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: 2 3 1. Determine the derivative to y² = x³ + y² + 2xy

A: Given problem:- Determine the derivative to y2 = x3 + y3 + 2xy

Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: Find the derivative of y with respect to x. 8x y = tan 3 - 24 O A. 64x2 + 9 O B. 64x2 + 9 24 Oc.…

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Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

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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: Find the derivative of the function. y = (x + 1)²(x² + 1) ~ 3 ...... - 2(x + 1)(2x² – 3x – 1) OA.…

A: Given:- y = (x+1)2(x2+1)-3 To find :- Derivative ol y

Q: Find the anti-derivative of the following: a.) f(x)=4x1/2-(4/x1/2) b.)…

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: 1-Find the first derivative of the following function f( x) 5 cos (10x) + x' – 2x – 6x+ 10 For x=2…

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Q: 2. Find the derivative using chain rule. (a) f(x) = 5(2.r + 3)3 Answer: (b) f(x) = (x - 4)*(2x +3)…

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Q: 3 Suppose 8 (x): 2(1- 5x)3 .What is the correct result of the derivative of g with respect to x? 45…

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Q: 1. Find the derivative of each of the following functions a) f(x) = cos5x %3D b) g(x) = cos 5x c)…

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Q: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

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Q: 1. Use the Power Rule and properties of derivatives to find the derivative of each function a) f(x)…

A: Here we have to find the derivative by using power rule and the properties of the derivative.

Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

Q: 6.) Find the derivative of the following functions a.) f(x)=- 7-3х |t +1 b.) f(x)=. -1 c.) f(x)= ean…

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Q: Find the derivative of the following using First Principle. 1) y = 1 2) у %3D х 3) f(x) = 5x3 %3D 4)…

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Q: 8) Find the derivatives of the following: a) f(x) = 4e* – 2x + 5 b) f(x) = ln 2x² c) f(x) = (4 – x)5

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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…

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Q: Suppose h(x) =23r +1 What is the correct result of the derivative of h with respect A h'(x) =3-23x +…

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Q: Suppose the derivative of f exists, and assume that f(2) = 1, and f'(2) = 2. Let g(x) = x2f(x), and…

A: Apply the product rule to find the derivative of g(x) and then substitute the given values as…

Q: 6. у3 In (x*+3х -1)2 V(5x+2) step1 step2

A: Derivative of function

Q: 6.) Find the derivative of the fonction 2 8- g'cx) =

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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: Find the derivative of the function y = In(x /x² + 14 X Vx²+14 1 Vx²+14 1 x²+14 x2+14

A: Topic:- derivatives  Note:- as per our guideline if more than one question uploaded than only first…

Q: Find the derivative of the function x³(2x + 1) f(x) = In x2 – 3 Select the correct answer below: O…

A: We can make it easier for you.

Q: Зх +1 a) y =- 1 b) g(x)= Jx -

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Q: 7. Find the second derivative of the following function: y = e** +In(7e¯* + 5x³) – 5²× +-

A: