If f′(4)=8, and g(x)=−2f(x), what is g′(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: Find the differential of the function y=(3-x8)1/2

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Q: 2) Find the derivative of the following: (8x² - 14x + 3) 8.r2 b) 5x-6 e

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Q: 1 Find the derivative of f(x) = v2 – 3xª 2 -4 |

A: We use chain rule to find derivative

Q: What is the first derivative with respect to x of f(x) = (x² – 4) (3x – 2)? a. (2x)(3) b. 6х (x + 2)…

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Q: a) 2xy dx+(1+x²)dy=0 b) y'+(4/x)y=x* ------by exact method ---by linear method

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Q: 5. If f(x)= 5x² + 2x+1 is an invertible function, find the slope of the tangent line to f^(x) at the…

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Q: In(ax) f(x) has a stationary point at Find a and b. bx 2' 3e,

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Q: 5. Solve xdx + ydy а? (хdу-ydx) x2+y2 using exact D.E method.

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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.

Q: 10. Find the derivative of y = V3x + 2. c) d) 3x a) 2V3x+2

A: Using derivatives

Q: Find the second derivatives:y^n for y=1/8x^4-1/3x^3+3/4x^2-3x+5 And f(x)=2x/5x-2

A: (i): Given : y=18x4-13x3+34x2-3x+5 f(x)=2x5x-2…

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 second derivative of the function y=x(x² – 1) (А) 4x(5х2 - 3) в) 2x(5x2 - 6) (с) (2х -…

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Q: 1. Eliminate the arbitrary constants on the given equation: y = C1 + C2e¯ -2x 2 Eliminato

A: Given

Q: Find the first, second, and third derivatives of the func- tion. W (t) = 5t² + 4e*.

A: NOTE: Refresh your page if you can't see any equations. . take the first derivative…

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

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

Q: Find the derivative of the function. 8x -8x y = -8x Bx + e -&x 8e&_ 8e

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Q: Find the second derivative of the function. f(x) = (3 + 2x)e−3x

A: Given:The given function is f(x)=(3+2x)e-3xTo find:The second derivative of function f(x)

Q: Find a particular solution for: y" - 3y' + 2y = te*

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

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Q: f. y=In(x8+1)

A: We will solve the problem

Q: V Solve usinog variaton of parameters or reduction of order (D²- 2D+1) y = e2"(e*+1)?

A: Solve by using variation of parameter  find auxiliary equation and then find wronskian and put in…

Q: 1. Eliminate the arbitrary constants in the equation given by: (x- a)(y – b) = 1 |

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Q: 3. Find the second derivative of f(x) = 2sin²(3x) а. 36сos? (3x) — 36sin? (3x) b. 36сos (3x) —…

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Q: Find the equation of the line tangent to the graph of f (x) = 1+ e-*for a. x = 0 b. x = -1

A: f(x) = 1 + e-x

Q: What is the anti-derivative of q(x) = 2e+5 3x 3 ? (Do not include the constant C in your answer.)

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Q: Find the derivative of the given function a. y= (2x-3 / 5x+1)4 b. 6x2-11x-x3+6 / -4x2+x+x3+6

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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: The derivative of y x²+1 is х2—1 =

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Q: In (4x+7) 1. Find the derivative of f(x) 5x e 10-18 x? Evaluate the integral: 5x-3x 5 6x*-3x?…

A: Please see the explanation below

Q: (x3-x)² .3. 2 5. у 3 х+1

A: We’ll answer the 5th question since we answer only one question at a time. Please submit a new…

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: 3. Find the general solution using the method of Variation of Parameters. y" + y = = sect

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Q: Determine the general solution of y" - y = 0 given y₁(x) = e-2x using reduction of order

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Q: Find the first derivatives of y = x3 – x + 2 e*

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Q: A particular solution of x¨ − 3x˙ + 2x = t2 + 1 is given by

A: given that x''-3x'+2x=t2+1. we need to find the particular solution for the given differential…

Q: Find the differential of the function. u = 3x4 + 4

A: The given function u=3x4+4

Q: Use variation of parameters to find the general solution of y′′−2y′+ 2y=(e^x)csc(x)

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Q: Suppose 8 (x) = V x²+1, What is the correct result of the second derivative of g with respect to x?…

A: The function is given by gx = x2+1 To evaluate: The expression of g''x.

Q: . A woman saved GH¢ 30,000 in a bank A, whose rate was x % per annum and GH¢ 20,000 in another bank…

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Q: find the following third derivative of y=(3x+2)2

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Q: determine the general solution of y''-y=0 given y1(x)=e-2x using reduction of orders

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Q: Use variation of parameters to find a particular solution of y'' - Y = 4e-x 1-e-2x Yp (x) =

A: Solution of the differential equation, By using the method of Variation of perameters

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

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Q: 1. Find the first derivative of the following. а. у%33x y = 3x² + 6 y = 2-1

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.