If f, g, and h are differentiable functions of x and 8 h (xg)' (xh)' (x²g)" (x²h)" A(x) = (xf)' (x²f)" f A'(x) = f' 80 80 g' h h' prove that where prime()

Q: Consider the following functions: f(x)=x√3-x; g(x) = x³ - 6x² + 3; h(x)= = ²-9 I² + 1 a) Use the…

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Q: Let f (x) and g(x) be differentiable functions in (a, continuous at a and b, and g(x) #0 in [a, b].…

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Q: 4. Let f be the function given by f(x) = 4-x. g is a function with derivative given by g'(x) =…

A: Given f( x ) = 4 - x

Q: Step 4 To find (f-l)'(x) use the theorem that states that if f is differentiable on an interval I…

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Q: 3. (a) If f(x) is an even function, pls prove that f'(x) is an odd function. (b)lf f(x) is an odd…

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Q: Let f and g be the functions in the table below. N X f(x) g(x) f'(x) g'(x) 1 3 2 4 6 2 1 3 5 7 3 2 1…

A: (a)Consider, F(x)=f(f(x))Differentiate with respect to x. (Use chain rule of…

Q: a) x³ - x f (x) = 2x² + x − 1 - b) f(x) = ax + b cx - d

A: Here we have to evaluate for a) and b) the value of f'(x).

Q: In (x2+1) f (x) x2+1

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Q: 83. Let f(x) = In (1 – x²). (a) State the domain of f. (b) Find f'(x). (c) State the domain of f'.…

A: Since you have asked multiple question and have not specified any question in particular, I will…

Q: Let f(x) = 5x² cos(2x). f'(x) = -10x²(2x) + 10x cos(2x) f'(5) = 0 f"(x) = -10x² sin (2x) + 10x…

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Q: True or false: If f is a differentiable function, then de [f(x³)] = f'(3x²) dx

A: The objective of the question is to verify the given statement about the derivative of a function…

Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f', g, and g'…

A: We have to find the value

Q: et f and g be the functions in the table below. f(x) g(x) f '(x) g'(x) 1 2 4 1 3 7 2 1 7 (a) If F(x)…

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Q: uppose that f and g are functions such that f(5)=3, f'(5)=-2, g(5)=4, and g'(5)=-5. nd h'(5) where h…

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