If f(x) = X S 1.² (2.3 (+³ 0 then f"(x) = || + 5t² + 7) dt

Q: Given the function below f(x) = 3 x³ – ²x² − 18 x + 3 a) Differentiate the functionƒ(x) = 3 x³ − 2…

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Q: 3x-4 -,x < 1 x+2 4. Given the function f (x) = . Calculate f'(1-) and f'(1+). In?x x+1

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Q: Show that if f (2) = −2 and f'(x) ≥ 5 forx &gt; 2, then f (4) ≥ 8.

A: Given that f (2) = −2 and f'(x) ≥ 5. And also, f(4) ≥ 8.

Q: f(1) = (r + 2x + 8)4

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Q: For the function f(x) = 7x – 3x+ 4, find f'"(x). Then find f"(0) and f''(6). f"(x) =(Simplify your…

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Q: If f(t) = (t + 7t + 3) (5t² + 6), find ƒ'(t). Find f'(5).

A: Given : ft = t2 + 7t + 35t2 + 6

Q: Compute and interpret f'(1) for each function above. f(r) = 6x2 + 3x 4 f'(1) = %3D

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Q: (x – 3' If f(x) = 4x + 3, find 4

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Q: 3. Find f'(x) for f(x) = 3x-4 2x+3

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Q: (2-9x³), find f'(x). Given f(x)= In (2-9x³), f'(x) =

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Q: Suppose f(x) √₂+² = √1+tdt 2x find f'(1).

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Q: If f(t) = 9t+1, find f"(5). %3D

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Q: Find f'(x) for f(x) = ex²+3x+¹¸

A: Given that f(x)=ex2+3x+1

Q: Find f(x) dx if S5 f(x) lx for x 2 5' for x < 5

A: Given- ∫07fxdx if 5    for x&lt;5x    for x≥5 To find- The value of the above integral.

Q: . If f(x) = V4x – 7, find f'(x).

A: we have ;  f(x)=4x-7;  we have to find f-1(x)

Q: f(x.y) = 7x?y",camate and af and ,campute

A: Given fx,y=7x2y4we have to find ∂f∂x =?    and   ∂f∂y=?

Q: If f(x) = 5x¹(²), find ƒ'(6) to 3 decimal places.

A: The given function,   f(x)=5xlnx

Q: If f(t) = (t + 5t + 4) (2t² + 2), find f'(t). Find f'(3).

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Q: Find f. f"(x) = -2 + 36x - 12x2, f(0) = 2, f'(0) = 18

A: Given, .Given,  f(0)=2, f'(0)=18.We know,

Q: Q/ Use Lagrangian polynomial to find f'(2.1) from the following table 1 2 3 f(x)| 10 17 22

A: Numbers of data point set is 3, so the degree of polynomial will be at most degree 2.

Q: 2. Determine the exact value of f'(2) for f(x) = (2e³ + 3e-6x)5.4,

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Q: / = 20. Evaluate f (a+ 2) for f(a) 3 4x-8'

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Q: Find f. f(x) = f"(x) = -2 + 18x - 12x², f(0) = 3, f'(0) = 12

A: Integration

Q: Given f(x) = x + 4, x < 0. Find (f-1)' (5) 10 1 2 | 29

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Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: Find f(2) if f (x) = e"

A: given equation f(x)=ex

Q: If f(t) = (t² + 3t+2) (5t² + 4), find f'(t). 201³ + 45t² + 32t Find f'(2). 40 X

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Q: 2x 5. F(x) = "(5t – 1) dt

A: Here, it is given that F(x)=∫x2x5t-1dt

Q: If f(t) = (t +5t + 2) (7t2 + 4), find f'(t). %3| Find f'(3).

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Q: Find f. f"(t)  = 3/√ t  ,f(4)  =20, f'(4)   =7

A: We have to find f where, f''t=3t, f4=20 and f'4=7. Integrating both sides, ∫f''t…