Solve the equation y' - y = f(t), 0 < t < 1 ={ t>1 where f(t) = 1 y(0)=0 " F(s) = 1 S+1 e-1_e-s 5+1 + S

Q: 2x + 8 Find f'(x) if f(x) x² + 3 f'(x)

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Q: and f' (0) = 0 and f(0) = –3. Find f' (x) = and find f(1)

A: Here we have, f''(x)=5x-2 ................................ (1). f'(0)=0 and f(0)=-3 We have to find…

Q: (x + 1) f' (x) = f(1) = 5 x,

A: Solution is given below:

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: f'(x)=12x3+1/x,    x>0,  f(1)=10   find f

A: Integrate both sides of f'x with respect to x as shown below:…

Q: f(x)=2x(10x/x2-1 +7x5 Finf f'(x)

A: We can solve the given problem using chain rule of derivative.

Q: Solve f'(t)-f(t)=2 where f(0) = 0

A: Given equation

Q: Let f(x) = |=| ƒ' (5). 0= √x-4 √x +4 Find f'(x).

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Q: f(x)= (x+2)² (x - 1) f'(x) = 3x(x+2) %3D f"(x) = 6x +6 %3D

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Q: Find f '(x) and f '(c). f(x) = (x³ + 4x)(2x³ + 4x – 5), C = 0 %3D

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Q: Find f'(x) and f'(c). Function f(x) = (x³ + 4x)(7x² + 5x − 6) f'(x) = - f'(c) = = Value of c 0 = 5

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Q: If f'(x)=8x' – 6x² +10x – 9 and f (1)=24, find f(x).

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Q: solve  w' + ((2w)/x) = x5,       w(0) = 1 what is w(1)

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Q: f(x)= 7tan-1(5sin(4x)) f'(x)=?

A: We have to find the derivative of the given function f(x)= 7tan-1(5sin(4x)).

Q: Longest interval for (t+2)y’’-(sint)y’+ty/t-4=e^2t/t y(-1)=0

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Q: Differentiate x4 - 4x + 3 - f(x) = Vx +1

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Q: The profit from the sale of a certain product is increasing at a rate given by P'(x) = 970x1/3,…

A: To find P(x) we have to integrate P'(x)

Q: Find f'(x) and find the values(s) of x where f'(x) = 0. f(x) = (2x – 21) (x² + 18) f'(x) =O

A: Given function, f(x)=2x-21x2+18 Multiply the function, f(x)=2x3+36x-21x2-378 For differentiation,…

Q: r(x) = 3x/4- x0.1/3 + 5/4x1.1 - 3 r'(x) =

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Q: Find f'(x) and f'(c). Function Value of c f(x) = (x³ + 2x)(3x³ + 5x – 4) c = 0 f'(x) = f'(c) =

A: fx = x3 + 2x3x3 + 5x - 4fx = 3x6 + 11x4 - 4x3 + 10x2 - 8xDifferentiating with respect to x on both…

Q: Find f'(x). Vx- 19 f(x) = e %3D

A: Given,            f(x) = ex-19

Q: Given f’(x) = 5cosx-16sinx    and f(0)= -1   Find f(x)

A: f’(x) = 5cosx-16sinx  We need to obtain the integral of this and satisfy the boundary condition.…

Q: Find g' (3) given that f(3) = – 5 and f' (3) = 10. %3D Enter the exact answers. (a) g(x) = 4x² –…

A: Given,           f3=-5 and f'3=10

Q: The rate at which users join is R'(t)=_.36t^2+3.84t+0.46 where t is months from (0<t<10) if there…

A: It is given that, the rate at which users join is R'(t)=_.36t^2+3.84t+0.46 where t is months from…

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: e = a and ey = b Find the value of tanh(x) + sinh(y) for a = 0.77 and b = 0.35 %3D

A: We will use the following formulas sinh(x)=ex-e-x2,  cosh(x)=ex+e-x2 and…

Q: a2u a2u =4 at2 au(x,0) où 0 sxs2 with (0,t) = u(2,t) = 0, = 0, %3D %3D %3D at x if 0<x <1 2-х т u(x,…

A: utt =4 uxx               :  0≤x≤2 u0,t = u2,t =0utx,0 =0   ux,0 =x      : 0≤x≤12-x : 1≤x≤2

Q: f"(x) = 5x – 1 and f'(0) = 3 and f(0) = -4. Find f'(x) = and find f(1) =

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Q: f" (x) = 7x – 1 and f'(-2) = -1 and f(-2) = -4. Find f'(r) = and find f(4) = %3D

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Q: f"(x) = 7x – 2 - and f'(-3) = –6 and f(-3) -2. Find f'(x) = and find f(4) =

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Q: Solve for k:  y(t) = y(0) * e^(kt* (1-t/p) )  (we know that y(0)=P/10)

A: We have given yt=y0·ekt·1-tp,  y0=p10 By dividing both sides of the equation by y(0), yty0=ekt·1-tp…