L{f(t)} F(s) Suppose that L{f'(t)} exists What's the value of: {-te¹0f'(t)} A) SF'(s) + F(s) B) (s 10) F'(s - 10) + F(s-10) - C) (s 10) F'(s - 10) + F(0) D) (s 10)F(s 10) - f(0) - - = with F a derivable function and that

Q: If f(x) = 6*, then f"(x) = A 6*(In6)3 B 6*(In6) (c) 6* 66 D (In6)3

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Q: If f (x) = Vsin¬1 (2x²) , then f' (x) = (sin¯"(2z²))*-/1–4z“ True False

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Q: Suppose that f(-5) = 0, f'(-5) = 4, f(8) = 9, f'(8) = 6, g(8) = -5, and g'(8) = 4. Compute (f o…

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Q: 12x + 10 Suppose that f(r) = Evaluate each of the following: f'(-2) = 5/2 %3D f' (5) = %3D

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Q: Syppese that f(5) =! f'(5)= 5)=-3 g(5)=7 and a) (5)

A: Given:- Suppose that f(5) = 1,f'(5)=4 ,g(5)=-3, g'(5)=7   a) (fg)'(5)   b) (f/g)'(5)   c) (g/f)'(5)

Q: Given f(x) = 1 –(5+ 10x) + (5 + 10x)² – 27 (5 + 10x)³ then f'(x) =, %3D - (5 + 10z) – ( 5 +…

A: f(x)=1-32(5+10x)+94(5+10x)2-278(5+10x)3 Then f'(x)=0-(32×10)+(94×2×5+10x×10)-(278×3×(5+10x)2×10)…

Q: Problem 2 (Exercise 2.10.2) Find the general solution using variation of parameters. Say whether the…

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Q: (0,F) (L.F) (L+ F, 0) (L+F+ LF, 0) 2. The following is the graph of f'(x).

A: From the graph,when 0≤x≤L, f'x=F Therefore, f(x)=∫f'xdx=∫F dx=Fx+cc being an integrating constant…

Q: 2x? + 5x + 4 (1 point) Find f' (16) if f(x) : f' (16) = -5/2

A: here is quation of derivative we have to derivate function F(x)= 2x3/2 + 5x1/2 + 4x-1/2 f'(x)=…

Q: Compute f’(-2) using shortcut rules. f(x) = 5x + 9

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Q: If f(5) = 1, f'(5) = 6, 9(5) = –3 and g' (5) = 2 determine: а) (f x 9) (5) b) (72)'(5).

A: Recall: Product Rule: fg'(x)=f'(x)g(x)+f(x)g'(x) Quotient rule: fg'(x)=g(x)f'(x)-f(x)g'(x)[g(x)]2

Q: f(t) = (2t^2 + 3t + 1)^-8 what is f’(

A: Given; ft=2t2+3t+1-8 Now we find the derivative of the given function, Differentiate with respect to…

Q: Suppose / (x)= - . What is the value of f "(-2)? A B D

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Q: If f(q)  = 50 + 50q gives profit when selling q units, and g(t) = t^2 - 12t + 1 gives the quantity…

A: Given: f ( q ) = 50 + 50 q , where f ( q )  is the profit on selling q units. g ( t ) = t 2 – 12 t +…

Q: x+3x + 2 If f(x) = then f'(1) = %3D O 3 07 0 5 0 4

A: By using differentiation property, we calculate the required value.

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

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

Q: Let f(y) = ⌊y⌋. Find a) f^-1({0}). b) f^−1({−1, 0, 1}). c) f^−1({y | 0 <y< 1}).

A: The given function f(y) is floor function:   The floor function is defined as: fy: The greatest…

Q: If f (x) 2e²x Then compute f" (0) + 2f' (0) + 2ƒ (0)

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Q: The graph of a continuous function f : [0,9] → R is given below. The function

A: given F(x)=∫0xf(x)dx

Q: Find f" (x) if f (x) = 3(2x¹ + 2x² + 1)¹. 48 (2x³ + x) (2x² + 2x² +1)³ 48 (6x² + 1) (2x² + 2x² + 1)²…

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Q: 5. Use the graph of ƒ '(x) shown and the fact that f(2) = 14 to find the value of f(12). f’(x) 8 3…

A: Notice that the graph of f'(x) on 2,8 is a upper semi circle with center (5,0) and radius 3.…

Q: If '(3) = -1 and h'(1) = 5, then "(r)dr= (A) -6 (B) 4 (C) 5 (D) 6 (E) 9 (F) 11

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Q: Giren f(e) = 2x+1 and g(4) = x*+ 2x-1, in (- () Then valute he difcene hen x=2.

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Q: Suppose that S(m)3(4#-4)*(32+ 1). Find f'(#), and then evaluate f' at # = 1 and # = -1 (1)= 1(-1)=

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Q: Let F(æ) = f(f(æ)) and G(x) = (F(x))² . You also know that f(3) = 10, f(10) = 2, f'(10) = 3, f'(3) =…

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Q: 140 士+0 9 -1 -1 cBook Pro * 1)

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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…

Q: 12) Use the graph to evaluate the expression. (a) f(1) y = f(x) (b) f-'(1) (c) f-'(4) -3 -! 3 (d)…

A: Given Data The equation is y=f(x)   (a) From the given graph, that value at x=1 is y=1. Hence the…

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…