The following table records some values of the differentiable functions f and g, as well as their derivatives f' and g'. X f(x) f'(x) g(x) g'(x) 1 9 4 4 8 2 5 8 7 3 Compute the value of (fg)'(1) Enter the exact value. (Your answer should be an integer for this one.) 3 7 9 1 9 4 ㅠ e 0 -11

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

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Q: et f and g denote differentiable functions. If f'(x) = g (x), then f(x) = g(x).

A:

Q: - For the following graphical representation of a function f(x): (1) Mark the points on the graph…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: Q1: In Leibnitz theorem, If f and g are functions of a variable x, then nth derivative of (f.g) can…

A:

Q: If f(x) = 6x²e*, then what is the derivative of f(x) with respect to x? 6xex O 12xe* О бхе"(x + 1) O…

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Q: Let f be a function defined on the closed interval -4sxs4. The graph of f', the derivative of f, is…

A: Let's find.

Q: (d) Use the following table to evaluate each derivative. I 0 1 2 f(x) 1 3 -2 g(x) f'(x) 1 2 4 -3 0.5…

A: Since you have posted multiple questions i can do first question as per our company guidelines,…

Q: 2. For the function, f(x), below, state the intervals of increase and decrease, the x-coordinates of…

A: The interval of increase: From the graph of the function, we can see that the function is increasing…

Q: what is a and b please?

A: Use chain rule to find the h ' (x) and g ' (x).

Q: If a function is defined by an equation G(x,y)=0 and could be found explicitly as y=f(x), then the…

A: We have to check

Q: Let g be the following function that gives the values of y in terms of the values of x.\\\\ g(x) =…

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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: Explain in your own words, how do you find the followings using first and second derivatives of…

A: To Explain: How can we find followings using first and second derivatives of function f(x):(a)…

Q: The graph of f', the derivative of f, is shown below. Determine the values of x, if any, at which…

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Q: 6. Suppose that f(x) = g(y) + x²y³ r + y (a) Use implicit differentiation to compute a formula for y…

A: We differentiate above function with respect to x and f(x) and  g(x) are function of x and y

Q: 4. f(x) = 5. 6. (X M 2x + 1)³ (x²-2) 10 100 ln(x+3), f(x) = (x) = { 4x² - 1, sin(xy) = x² + y³ if x…

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Q: Step 2: Step 3: Sten 4:

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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: a) f(x)=x44 b) g(x)=(3-x+4x²)(2x²- c) h(x) = x² – 3x 2-x²

A: ddxxn=nxn-1 ddxfxgx=gxf'x-fxgxgx2 [As per the guidelines I am answering only first 3 parts of the…