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: 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: If f(x) = (3x +8) find f'(z). Find f'(1).

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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: Given f"(x)=8x-5 and f'(0) = 4 and f(0) = 3.

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

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

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

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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: Differentiate the function and simplify the answer. f(x) = 2x e2r'+x² Select one: f'(x) = 2xe2r³+x?…

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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: (2/x+1)(x– 1) Find the f'(x) of the function f(x) = x+3

A: Given, f(x) = 2x+1x-1x+3 f(x) = 2x32-2x12+x-1x+3 We know that ddxxn = nxn-1  and quotient rule of…