PROBLEM A. f"(t) + 3f'(t) + 2f(t) = 0 where, f(0) 1 and f'(0) = 0

Q: If f(x) + x2[f(x)]ª = 18 and f(1) = 2, find f '(1). %3D f '(1) =

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Q: (1) If f(x) = x¹0, then f'(x) =

A: According to bartleby guide line we do only first part of multiple questions. please re-post other…

Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

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Q: Suppose f(x) f'(2) = ex x² +5 . Find:

A: Given: f(x)=exx2+5

Q: Find f. f"(x) = 8x + 5, f(1) = 9, f'(1) = 3

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Q: b) y =1+ f(z)=2x-2 O 1ks f-(z)=-1 O 2 34s (2)=2x-1

A: Step 1 Replace y with x and x with y  Step 2 Then solve for y in this equation  Step 3 Replace y…

Q: Given f"(x) = 6x - 1 and f'(-3) = -3 and f(-3) = -4 Find f'(x) =  and find f(1)=

A: Given f''x = 6x-1    and f'-3 =-3                                  f-3=-4Now  We know f'x = ∫f''xdx…

Q: If f(x) = (a + 3r + 2)", then f'(x) - f'(1) =

A: To find out f'(x) and f'(1).  Derivative rule : ddxxn=nxn-1

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: If f(3) = 1, f'(3) = 1, g(3) = 1 and g' (3) = -2, then P dz g(x) I f(z) %3D Answer:

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Q: If f'(x) = 3x2 + 2x and f(2) = 3, then f(1) = (A) – 10 (B) -7 (C) 10 (D) 13

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Q: GivenF(x) = h(f(g(x))), g(1) = 2, g′(1) = 3, f(2) = 4, h'(4) = 1 and f'(2) = 6, findF′(1)

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Q: 1. If f(x) = 5x4 - 6x² + 4x - 2 find f'(x) and f'(2).

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Q: f (x) You are given h(x) = f(g(x)); p(x) = f(x)·g(x); q(x) = g(x) and the following values f(2) = 1,…

A: Given : hx = fgxpx = fx·gxqx = fxgx

Q: 225 350 Duval Street B 125 400 + х Monroe Street 800 +300 D 250 600 he above figure shows a typical…

A: As the number of vehicles from the road and crossing is represented  using the number of vehicles…

Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f '(1). f '(1) =

A: Given:  f(x) + x2 [f(x)]3 = 10 and f(1) = 2

Q: If h (x) = (x² – 2x 43 04/0 0 - 12/25 3 00 - (x² – 2x − 1) ³, then h' (0) =? - 43

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Q: If f(x) + x²[f(x)]³ = 10 and f(1) = 2, find f '(1). f(1) = -28 X

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Q: 6. If f(x)=3x' -+ 4 + 4x +1, find f(x) and f"(x).

A: Given query is to find the Indicated derivative.

Q: f(2)=-3. f'(2) = 10. g(2)=4, and g'(2) = 1. then evaluate (fg)' at x = 2

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Q: 12 If f(t) = find f'(t). f'(t) =

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Q: If we let f(x) = 1-4x/1+4x What are.... f’(5) = f”(5) = f”’(5) =

A: we have to find derivative at that point

Q: Find f. 4 f'(x) = 1- Ex) = %3D

A: This is a problem related to integral. Based on the given differential equation we will calculate…

Q: If f(x) = f'(x) = f'(1) = 7x + 5 6x + 2 3 find:

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Q: If F(x) = f(g(x)),

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Q: 12) Find a function f(x)with the f ollowing properties: 4 3 f'(x) = 2e2* –+ and f (1) = -2 %D

A: Given that: f'(x)=2e2x-4x+3x2 and f(1)=-2

Q: 1. f(x) = 6x + 15 find f'(x) Answer:

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Q: Find f'(x). f(x) = (x² + 1) * f"(x) = %3D

A: Find f''(x)

Q: If f(2)=1, f'(2)=5, g(2)=2, and g’(2)=-3, then d *) |x=2

A: Given,          f2=1, f'2=5 , g2=2 and g'2=-3

Q: If f(x) = f'(2) 3x + 1 x + 1 then:

A: given  f(x)=3x+1x+1dxndx=nxn-1d dx(ab)=b(dadx)-a(dbdx)b2

Q: Suppose H(x) = f(g(x)) and %3D f(14) = 3 f' (2) = 13 g(14) = 2 d (14) = 4 Find H' (14)

A: Chain rule of differentiation:

Q: If f(x) = (2² + 5x + 3)“, then s'(#) - [ f'(x) -

A: To find the derivative of the given function, we need to use chain rule of differentiation and some…

Q: If f(x) = x° + x³ + x, find f ¯'(3) and f(f¯'(2)). %3D

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Q: 0. f"(x) = 12x; f(1) = 2 and f'(1) = -2 3. ((a)

A: Given query is to find the function.

Q: If f(x) = 5x4 – 2x3 – x² + 3x – 1, then f'(0) = d2 ;f(0) = f''(x)= d4 ¡f(x)= 4 dx

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