If f(0) = 1, ƒ'(0) = -1. g(0) = –1, g (0) = –3, and h(x) = (x² + f(x))g(x) then h' (0) =... O -2 O 2 O 1 O -1

Q: Given f''(x) = 3x – 6 and f'(– 3) = 2 and f( – 3) = - 1. – 1. Find f'(x) = and find f(2) =

A: The objective is to find f'(x) and f(2).

Q: 3. (a) (10) Let g(x) Find g'(x). Don't try to simplify your answer. In(4.x) – cos(2x)

A: Given function g(x) is differentiate w.r.t x as written below:

Q: 45. If F(x) = f(g(x)), where ƒ(−2) = 8, ƒ'(−2) = 4, ƒ'(5) = 3, g(5) = −2, and g′(5) = 6, find F'(5).

A:

Q: 4. Let g(2) = 3 and g'(2)=1. Find g(-2) and g'(-2) assuming a) g(x) is an even function. b) g(x) is…

A: The objective of this question is to find the value of the function g at -2, denoted as g(-2), and…

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

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Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

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Q: If h(x) = f (g(x)), where f(0) = 7, g(0) = - 1, f'(0) = 0, g'(0) = - 3, f(- 1) = - 3, g(- 1) = 2,…

A: We have hx=fgx

Q: Suppose f(x) f'(2) = ex x² +5 . Find:

A: Given: f(x)=exx2+5

Q: 1. f (x² + 1)(x² + 3x) dx

A: To evaluate the given integral.∫x2+1x3+3x4dx

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: 3. Given f(4) = 1, f'(4) = 3, g(4) = -2, g'(4) = -5. %3D %3D If h(x) (2x3+1)f (x) Vxg(x) calculate…

A: Given that, hx=2x3+1fxxgx Differentiating with respect to x we get,…

Q: 6. Let f(x) = -5x¹ and g(x) = 2x + x. If h is the function defined by h(x) = f(g(x)), which of the…

A:

Q: 4. Given a function f(x) that is written as f(x) = h' (2) = 4, then f'(2) =? g(x) h(x), if g(2) = 2,…

A: 4. Given a function f(x) that is written as f(x) =g(x)·h(x) , if g(2) =2 , h(2)=-2 ,g'(2)=-3 and…

Q: 1. Find the function f(x) if f'(x) = 3x² – 2.x +5 and f(0) = 5 %3D

A: Given, f'x=3x2-2x+5f0=5 To find, The function f(x).

Q: GivenF(x) = h(f(g(x))), g(1) = 2, g′(1) = 3, f(2) = 4, h'(4) = 1 and f'(2) = 6, findF′(1)

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Q: Given f(4) = 13, f '(4) = 19, g(4) = 7, and g'(4) = – 10, find the value of h'(4) based on the…

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Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 = ƒ'(2) = g'(2)…

A:

Q: For the following exercises, assume that f(x) and g(x) are both differentiable functions for all x.…

A:

Q: 9. [f(x)dx -1

A: Find the integral from the given graph

Q: The derivative of f(a) = -a* - 4 * – 2 a2 - a is O f(a) = -4 a – 12 a - 4 a2 O f(a) = -4 a - 3 a2 -…

A: We have to find the derivative of f(x) = -x4 - 4x3 - 2x2 - x.

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)…

A:

Q: If f be the function defined by f (x) = x³ + x. lf g (x) = f−¹ (x) and g (2) = 1, what is the value…

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Q: If x f(x)+x g(X)= sin x, for nonzero x, then f''(X) + g''(x) is %3D

A:

Q: If f(x) = and g(æ) = f-'(x), find g' (x). O g'(x) = 3z2 O g (x) = O g (¤) = - O g(x) = - 2z

A:

Q: If we let f(x) = 1-4x/1+4x What are.... f’(5) = f”(5) = f”’(5) =

A: we have to find derivative at that point

Q: 3. Differentiate. x²e* f(x)%3= x² + ex

A:

Q: If f(x) = (x+1)/(x-1), where x # 1, determine f '(1). %3D

A: derivative of fx=x+1x-1 at x=1

Q: If f(x)=2x-3, and g(x) is a function such that g"(0) = 4 and (fg)"(0) = -4, then g'(0) =

A:

Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

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Q: 10. Use the given information to find f"(2) of the function f(x)=g(x)h(x). g(2)= 3 and g'(2)…

A:

Q: x2 with g(1) = 2 and g'(1) = 3. Find the value of f"(1). Suppose that f(x) = g(x)

A: Explanation of the answer is as follows