Consider the function Suppose that g(6) = ƒ' (6) = f(x) = (1 + sin(x)) (*) -9 and g'(6) - 4.

Q: g(x) = 2x + 3 X - 5 Given the functions find g'(x)

A: Inverse of function problem....

Q: Let f'(x) = f(x) = = 4x √8 - 6x

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Q: Let f(x) = 2ln(sin(x)) ƒ''(x) =

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Q: If  f(x) = x2/(1+ x) , find f" (1)

A: We use quotient rule to find f'(x)

Q: 2x? + ху? %3D 1

A: Given function is 2x2+xy2=1. BY product rule of differentiation, we have ddxuv=uddxv+vddxu…

Q: Consider the function f(x) whose second derivative is ƒ''(x) = 9x + 6 sin(x). If ƒ(0) = 4 and f'(0)…

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Q: Find f '(x) and f "(x). x2 7 + 4x f(x) =

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Q: 4) Find the derivative of f(x) = (5x² - 3)² in two different ways.

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Q: Let f and g be functions that satisfy f'(2) = -6 and g'(2) = 9. Find h'(2) for each function h given…

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Q: Find f''(x) for the function. f(x) = 8x³ - 2x² +4 OA. 32x-4 B. 4x-32 C. 48x-4 OD. 4x-48

A: Givenf(x) = 8x³ - 2x² + 4

Q: Find the function f(x) if f''(x)=12x-6, f'(2)=4, and f(2)=-4

A: The second derivative of the function is given by f"(x_=12x-6, f'(2)=4 and f(2)=-4.

Q: Find f'(x) for the given f(x).

A: Our aim is to differentiate the following function f(x) given below:-

Q: Find f'(-2) for f(x) x² +1

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Q: The functionf(x) is Find the first derivative in fa Set up a number line with t increasing,…

A: The given function is fx=3x5-5x4. Find the first derivative of the function by the power rule of…

Q: Calculate f"'(-1) for f(x) = 3x 5 - 2x 2 + 1x- 2 .

A: Consider the given function, fx=3x5-2x2+1x-2 here the objective is to find the value of the third…

Q: Letf, g be functions. Suppose we know that ƒ(−6) = 4, ƒ' (−6) = −4, g(−6) = −4, g′(−6) = −3. Using…

A: The given function and derivative values,.The aim is to find the value of  where .

Q: Suppose that ƒ(x) and g(x) are two functions and we know that: ƒ(-3) = 2 g(-3) = 5 ƒ'(−3) = −1…

A: Suppose that fx and gx are two functions and we know that,  f-3=2g-3=5f'-3=-1g'-3=-2 To find the…