Find an antiderivative F(x) of the function f(x) = 5 sin(x) such that F F(7) 2 F(x): Now, find a different antiderivative G(x) of the function f(x) = 5 sin(x) such that G G(x) = 3. G (7) = -8. =

Q: For the function f(x) = -7 e X, find f"(x), f''(0), f'"(9), and f''(-9). f"(x) = (Type an exact…

A: The objective is to solve the above question.

Q: Let f (x) = sin 2x and g (x) = Vx. Find formulas for f (g (x)) and g (f (x)). f (g(x)) = ? Edit g (f…

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Q: Find the derivative, f'(x), for f(x) = S dr 3 sinr+2 (₁²³+√7) X A f(x) = B f(x)= −sinx − 2 x²³+√√x X…

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Q: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

Q: Let f(x) = sin2x and g(x) = cos2x. Determine whether h(x) is in span(j(x), g(x) ) h(x) = cos 2x

A: Given  f(x) = sin2x, g(x) = cos2x and h(x) = cos2x Then, we have to determine h(x) is in span(f(x),…

Q: Find f'(x) and simplify. f(x)= x x+2 Which of the following shows the correct application of the…

A: F′(x)=(x+2)22​Explanation:If you have any questions let me know in comment box thankyou for your…

Q: Si f(x) es una función con antiderivada F(x), determine la afirmación correcta. Jise) – 21° d |(2) –…

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Q: Let f(x) = 5Vx and g(x)= 4 + sin x. (a) Find (f • 9(x) and (f ° g'(x). (b) Find (g ° )(x) and (gº…

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Q: For the function f(x)=3x² - 2x+7, find f''(x). Then find f’’(0) and f’’(8). f''(x)=(Simplify your…

A: See this solution in below.

Q: For the function f(x) = In (x + 3), find f"(x), f'"(0), f''(2), and f"(- 4). 1 f"(x) = (x + 3)2 (Use…

A: Given function     f(x) = ln(x+3)

Q: Find f" (x), given f(x) = sec x. O f" (x) = sec³ x tan x Of" (x) = sec a tanz Of" (x) = sec³ x + sec…

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Q: f(x) 132. Let h (x) = g(x) Find a. h' (1), b. h' (3) , and с. h' (4).

A: Given

Q: nd an example of a function f(x) such that the third derivative f"(x) is equal to 0 for all x, and…

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Q: Find f if f"(x) = 2 + cos(x), f(0) = -9, f(pi/2)=9 f(x) =

A: Solution of given question is followed by:

Q: Calculate h(x) if f(x) = x+3 and g(x) = sin(3x). Let h(x) = g(f(x)). What is h-1(x)? What is…

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Q: For f(x) = x? – 2x – 1, find f(2), f'(2), and f(3) – f(2). - a. f(2) = -1 b. f'(2) = c. f(3) – f(2)

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Q: Assuming functions g and h are differentiable, find  f(x).  f(x) = cos4(g(x))  f(x) = h(xex )…

A: The given functions are,

Q: Find f if f"(x) = 2 + cos(x), f(0) = -10, f(x/2) = 4. %D %3D f(x) = iii

A: Recall: ∫xn dx= xn+1n+1+c; where c is an integration constant. ∫sinx dx= - cos(x)+c; where c is an…