Question

Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x = 3. Find the derivatives with respect to x of the combinations below at the given values of x. | x | f(x) | g(x) | f'(x) | g'(x) | |---|---|---|---|---| | 2 | 6 | 2 | 1/9 | -4 | | 3 | 1 | -6 | 3? | 5 | a. 2f(x), x = 2 b. f(x) + g(x), x = 3 c. f(x) * g(x), x = 3 d. f(x) / g(x), x = 2 e. f(g(x)), x = 2 f. sqrt(f(x)), x = 2 g. 1 / g^2(x), x = 3 h. sqrt(f^2(x) + g^2(x)), x = 2 

          Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x = 3. Find the derivatives with respect to x of the combinations below at the given values of x.

| x | f(x) | g(x) | f'(x) | g'(x) |
|---|---|---|---|---|
| 2 | 6 | 2 | 1/9 | -4 |
| 3 | 1 | -6 | 3? | 5 |

a. 2f(x), x = 2
b. f(x) + g(x), x = 3
c. f(x) * g(x), x = 3
d. f(x) / g(x), x = 2
e. f(g(x)), x = 2
f. sqrt(f(x)), x = 2
g. 1 / g^2(x), x = 3
h. sqrt(f^2(x) + g^2(x)), x = 2
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Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x = 3. Find the derivatives with respect to x of the combinations below at the given values of x. | x | f(x) | g(x) | f'(x) | g'(x) | |—|—|—|—|—| | 2 | 6 | 2 | 1/9 | -4 | | 3 | 1 | -6 | 3? | 5 | a. 2f(x), x = 2 b. f(x) + g(x), x = 3 c. f(x) * g(x), x = 3 d. f(x) / g(x), x = 2 e. f(g(x)), x = 2 f. sqrt(f(x)), x = 2 g. 1 / g^2(x), x = 3 h. sqrt(f^2(x) + g^2(x)), x = 2

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Suppose that functions f and g and their derivatives with respect to x have the values shown to the right at x = 2 and x = 3. Find the derivatives with respect to x of the combinations below at the given values of x.
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Transcript

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00:01 Here, we're given a function, well, two functions and its derivatives in a chart.
00:05 And we want to find the derivative of another function that's a combination of these at another given point.
00:11 So say, for example, we have f of x divided by g of x.
00:17 Now, i pick this one because i think it's the hardest of all the ones that you have listed out here.
00:21 What we have to do here is just simply identify what rule we have to use.
00:25 In this case, to take the derivative, we need the quotient rule, which says we're going to take the derivative of the top.
00:30 Times the bottom minus the top unchanged times the bottom derivative all over the bottom squared.
00:40 So now i just need to find that value at x equals 2.
00:44 So that means i need to find f prime of 2, g of 2 minus f of 2, g prime of 2, all over g of 2 squared.
00:57 And the table gives us all those values...
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