f L{f(t)} = y(s), then L{ƒ'(t)} = sy(s) + y(0) y(s) - y(0) s²y(s) sy(s) - y(0) خبار 2 الخيار رقم 1

Q: 1 (D²-3³e*f"(x) =e³* (x) (D² - 3) O O

A: If we take f(x) =x^3/6 then the equation doesnt hold

Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

Q: If f(t) = (2t - ), find ƒ' (t).

A:

Q: If f(x) = (5x +7)°, then the value of (f-1 (x))' at (f(-1),-1) is

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Q: TLP iadade mnts & smt Findf F'(t) =sec(t) (seclE)+ tan (ED), -st < f- FCt) = -<ts f (--7 2.

A: We simplify f'(t) by expanding  To find f(t) we integrate f'(t) C=integrating constant

Q: Find y as a function of x if y(1) = 1, y'(1) = 4. y = x²y"-7xy' + 16y=x6,

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Q: Let f(x) = (x³ +2x+4)* ƒ'(x) = = ƒ'(1) =

A: The function is f(x)=(x3+2x+4)4the aim is to find the derivative then the derivative of the function…

Q: x"+x=2cos(t)

A: The general solution of a differential equation is the sum of the complementary function and the…

Q: Find y as a function of x if x'y" + 5xy' + 4y = 0, y(1) = 9, y'(1) = -2. y =

A: Solution :-

Q: f'(x) 2 F(x) d If f is differentiable, then VF(x) dx

A:

Q: g(t) g'(t) h(t) h'(t) -10 6. -1 -9 1 -3 1 -3 5 2 4 14 -1 -1/4 3 2 -1.5 -2 4 8 1/2 1 find: f '(1)…

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Q: Prévicy (Find y as a function oft if 144y" – 408y' + 289y = 0, | y(0) = 8, y' (0) = 4. y =

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Q: Find the domain of the function g(x) = /1 – x ln x

A: We have to find domain

Q: If f(t) = (t² + 6t + 7) (7t² + 4), find ƒ'(t). Find f'(2).

A: INTRODUCTION A function's differentiation can be used to display the rate of change of a function at…

Q: Consider the function h(z), for which h(4) = -12 and h'(4) = -7. %3D h(z) Find f'(4) for the…

A: To Determine: find f'4 Given: consider the function h(x) for which h4=-12 and h'4=-7 also…

Q: * Find y as a function of æ if y" – 8y" – y' + 8y = 0, y(0) = 4, y'(0) = -6, y" (0) = 130. y(x) =

A:

Q: Find y as a function of a if y(0) = 6, y'(0) = 24, y"(0) = 108. y" + 36y' = 0,

A: y′′′+36y′=0y(0)=6,y′(0)=24,y′′(0)=108.The characteristic equation…

Q: Find the range and domain of the functions (1) f (x, y) = sin-(y-x)

A: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the question…

Q: Find y' (-1) if y = In (a² + 5)° (2 – 4æ)®

A: I have stated the used formulas in the solution

Q: If f(x) = 7+ f'(x) = Find f'(3). ƒ'(3) = 5 X + 2 x2 I find f'(x).

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Q: Find y as a function of x if y(0) = 13, y' (0) = 22, y" (0) = 27. y(x) = y" - 15y" +56y' = 42e*,

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Q: Find y' and y". (x – y)3 = x – xy + 1

A: Topic :- Derivative

Q: 5-s s² + 4s-5 (A) Find L¹(F(s)}, knowing that: F(s)=- DA

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Q: dy 2²+1 Use the quotient rule to find the derivative of the function y = dx О А. dy 1 = 2x(x+ V) –…

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Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

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Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: Suppose F(8) = 5, F(9)= -23, and - 9 f6f (x) d Your Answer: Answer dx= F'(x) = f(x).

A:

Q: 6. FinD F(S) if f(t)= t· cost

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Q: Let P(x) = F(x)G(x) and Q(x) , where F and G are the functions whose graphs are shown. G(x)' F 4 2 G…

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Q: Find f'(1) ir f (x) = In(x2 + 1).

A: We use chain rule

Q: find y as a function of x if y'" + 81y' - = 0 where y(0) = 1, y'(0) = 81, y"(0) = 324

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Q: 16.) P Cn, f); For exomple, how do you compute PCG, 3) example, compute C CG, 3) or C§)

A: Permutation is number of ways of selecting and arrangement of r items out of n items. Combination is…

Q: True or False if f'(x) = i +t2j and f(0) = j - k then  f(x) = ti + (t3/3+1)j

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Q: If f(x, y): = x²y (5x - y²) "I find the following.

A: