y(t) = y" - 7y' + 6y = et + s(t - 7) + 6(t-9), y(0) = 0, y'(0) = 0 ) + ( [ ])2(x-7)+ ( [ 1) 2(t-1

Q: tx' 3 - - (³ 4) X X = C1 (1) +02 10 + ()

A:

Q: f"(x) = 4x – 2 and f'(-3) = -3 and f(-3) = –6. Find f' (x) = %3D and find f(4) :

A: f''(x)=4x-2 f'(-3)=-3 , f(-3)=-6

Q: If ƒ(t) = (t² + 6t + 7) (7t² + 2), find f'(t). Find f'(2).

A:

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A:

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: f(x) = (6x – 4)* - (4x² + 5)³. f'(x) =

A: Using product rule and chain rule of derivative,

Q: Find ƒ(x) if ƒ'(x) = 3x² - 4x + 4 and ƒ( − 1) – – 4. ƒ(x)

A: F

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Q: {In(æ² + xy+y³)} Find

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A: In mathematics, precalculus is a set of course that includes algebra and trigonometry to prepare…

Q: (4³ + 6)%,' = x^(,5 + 6)5 y

A:

Q: f"(x) = 6x – 2 | and f' (-2) = 3 and f(-2) = 6. Find f' (x) = and find f(4) =

A:

Q: Find the y_(p ) of y^(')'-5y^(')-6y=18x^(2)+12e^(2x) 2

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Q: y^(5)−4y^(4)+4y^(3)=0 Use lower case c1,c2,c3,c4, and c5 for the arbitrary constants. y(t)=

A: y^(5)−4y^(4)+4y^(3)=0Use lower case c1,c2,c3,c4, and c5 for the arbitrary constants.y(t)=

Q: 3. y'+7=(-2x+ y)';y(0) = 0

A:

Q: IF F"(X)=12X^2+24X-6 ,  F'(1)=10,   F(2)=20 , determine the function f.

A:

Q: +8x-x +2x +1 (x² + 3)(x' +1)

A: SImplification of the given function helps to find the required integrated function. The partial…

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A: Simply and differentiate to get the answer.

Q: Show that F(x) = 4x² + 6x +5 is anti-derivatives of f(x) = 8x + 6

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Q: f(x) then: f'(x) = f'(1) -

A: We are asked to find the derivatives of the function.

Q: Find the derivative of y = 5x²sec 1(2x-3). O y'= 10x sec-¹(2x-3) + O y'= 10x sec-¹(2x-3) + O y'=…

A:

Q: Evaluate the integral. 4 1 dx 2x Ji

A:

Q: (x? + 3x — 45)dх J«+ 3)(х + 12)(4х — 3)

A:

Q: Determine y'of (3x + 1)*(2x – 1)³

A:

Q: Find dim(Q(a)), where

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Q: 3 +5 - dx =

A:

Q: Find f. f"(x) = 48x2 + 2x + 6, f(1) = 5, f'(1) = -5 %3D

A: Given,  f''x =48x2+2x+6  f'1 =-5 f1 = 5  We have to find fx

Q: 8) y'+y=17 sin(2t), y(0) =-1.

A:

Q: y""+12y" +36y=0; y (0) = 0; y'(0) = 1;y" (0) = -7 ✓y""+y" - 2y=0 y" - 4y'-5y=0; y ( 1) = 0; y' (1)=2…

A:

Q: 3) Find y"(0), where y = 4x + 2x + 3

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

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A:

Q: 140 士+0 9 -1 -1 cBook Pro * 1)

A:

Q: f(x) = 4sin (1-3x2) + xcosx-9, then f'(x) = -24xcos (1-3x2)+cosx-xsinx True O False

A:

Q: Find the derivative of f(z) = (x³ + 5)(z³ – 5) %3D (8z")(5x*) (8z +5)(z – 5) + (z³ + 5)(5x* – 5) (8z…

A: We need to use the product rule.

Q: |_y'''+12y" +36y'=0; y (0) = 0; y'(0) = 1;y" (0) = − 7

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: y(t)=(2t-1)(5t-5)^-1, find y'(t)

A: Using Quotient Rule of Derivatives

Q: 1) f(x)= (x3+2x)6, Then Find f''(x)

A: As per our guidelines we are suppose to solve first question. Kindly repost the other question as…