let be a defferentlable function such that gand g take the following values. gen/3)=1, g/3) = 0, g(2)= 2, g'(2)=4 ) ut f(x)= g6) Since) ) eompute fl/3 D Compute h'(2)4 h)= 12g)

Q: Show that the derivative of FOx) =x² is f'x)=2x using the defimition

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Q: sin () (cos (t*) + t)dt %3D (2), NOTE: Enter a function as your answer. Make sure that your syntax…

A: In the given question, the Fundamental Theorem of Calculus Part I is applied. ∫afxgtdt=gfx·f'x

Q: 5) Find the derivative of each of the following functions. a) f(x) = (3x- 6x - 7) %3D b) g(t) = V4t-…

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Q: Find f such that f'(x) = f(x) = √x¹ f(1) = 13. ***

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Q: a) y = −8x² + 4x¯¹ − 2 b) f(x)=√√x - √x 5 c) g(x) = x³

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Q: 4) The population of frogs has been declining in North Dakota. At one lake, researchers found there…

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Q: 25 (6x + 5)³ But Do NOT use the Quotient Rule. a) Let f(x) = = f'(x) = Find f'(x). b) Let g(x) = 6…

A: We have to find the firstd erivative of the given functions.Recall some basic formulas: ddxxn=nxn-1…

Q: Find and interpret f'( – 2) and f''(– 2). 3 f(x) =

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Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. rtan(x) 5t…

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Q: Find the original function f(x) from given equation f'''(x)

A: We can solve this as follows:

Q: 1 6. Find the derivative of f(x)= 1 at the point 8, Vx+1

A: Given

Q: Suppose that S(m)3(4#-4)*(32+ 1). Find f'(#), and then evaluate f' at # = 1 and # = -1 (1)= 1(-1)=

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Q: f(x) = 1/(1+e^1/x) a) Find the domain of f. b) Find the inverse of f.  c) Find the range of f.

A: a) Domain is possible values of x.For 1/x we can not have zero in denominator. So, domain is all…

Q: Find the second derivative of the function f(t)= t³sect. Of"(t)= t³sect(20+tsect+10ttant+ftan²t)…

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Q: b) caleulate the lerivative of f Cx) by USing product rule flx) = (2-3x)? the

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