If F(x) f(g(x)), where f(1) = 8, f '(1) = 3, f '(-1) = 5, g(-1) = 1, and g'(-1) = 4, find F '(-1). %3D

Q: 4 X- - 5x +4. %3D Find f'(x), f"(x), and f (x) for f(x) = f'(x) = f"(x) =

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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: Find y=f(x), if f''(x)=3x^2, f'(0)=-7 and f(0)=2.

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Q: Find f. f'(x)  = x-1/3    ,f(1)  =1, f(-1)  = -1

A: To find f(x) we integrate f'(x) C=integrating constant

Q: Find f. f"(x) = 6 – 6x – 60x³, f(0) = 2, f'(0) = 3 %D f(x) = %3D

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Q: If f'(x)=7x x-4 and f(4)= - 5, then what is f(5)?

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Q: Find f'(x)) D f(x) (2) f(x) 3x³ +5x²12-2 2 6x -3x + 2x12 2

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Q: Find f(x) if f "(x) = x -3/2, f ' (4) = 1  and f(4) = 4.

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Q: Find  f '(a). f(x) =    1 − 4x

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Q: y' = x2y2/x2+y2 ; is this function seperable or non-seperable

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Q: Find f'(a). f(x) = 7x - 8x + 6| %3D

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Q: Given f''(x) = 4x – 6 and f'( – 1) = – 2 and f( – 1) = 4. Find f'(x) = and find f(2)

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Q: If f(x) = 6 + Find f'(3). X 3 x² " find ƒ'(x).

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Q: Please

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

A: Given fx=x5+2x5x5+5x-4c=0

Q: Evaluate the integral. 4 1 dx 2x Ji

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Q: First find f' and then find f. f"(x) = 10x³ + 2x? – 5x – 7, - f'(1) = –6, f(1) = -3. f'(x) = f(x) =

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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) 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: If f(x) = (5x +6) find f'(x). Find f'(3).

A: topic - derivative of a function

Q: Find y=f(x) if f''(x)=4x^2, f'(0)=3, and f(0)=2.

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Q: Given f'"(1) = 9x +4 and f'(- 2) = 2 and f(- 2) = - 6. - Find f'(x) = and find f(4)

A: Given  f''x=9x+4          f'-2=-2  and f-2=-6          f'x=∫f''x dx+C                =∫ 9x+4  dx+C…

Q: B. f"(x)=8x³ +5, ƒ(1)=0, ƒ'(1)=8

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Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: Find f '(x) and F "(x). (x) = 5+ 2x 10x + 2x f'(x) %3D (5 + 2x)? 10 - 4x f "(x) (5 + 2x)?

A: Given:

Q: Find ƒ'(−1) if 4x( f(x))² + 4x³ƒ(x) = 0 and ƒ(−1) = −1. ƒ'(−1) =

A: we need to find out the f'(-1).

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.