Question

Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. h'(3) b. p'(4) X 1 2 3 4 f(x) 4 3 1 2 f'(x) -4 -2 -5 -3 g(x) 3 1 2 4 g'(x) frac{1}{8} frac{5}{8} frac{7}{8} frac{3}{8}

          Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives.
a. h'(3)
b. p'(4)
X
1
2
3
4
f(x)
4
3
1
2
f'(x)
-4
-2
-5
-3
g(x)
3
1
2
4
g'(x)
frac{1}{8}
frac{5}{8}
frac{7}{8}
frac{3}{8}

$Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to compute the following derivatives. a. h'(3) b. p'(4) X 1 2 3 4 f(x) 4 3 1 2 f'(x) -4 -2 -5 -3 g(x) 3 1 2 4 g'(x) frac18 frac58 frac78 frac38$

Added by Erika O.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shannon K

03/15/2022

Step 1

Given that g(3) = 2 and g'(3) = 5, we have g'(3) = 5. Now, h'(x) = f'(g(x)) * g'(x). Substitute x = 3 into the formula: h'(3) = f'(g(3)) * g'(3) = f'(2) * 5. From the table, we see that f'(2) = 3. Therefore, h'(3) = 3 * 5 = 15. Show more…

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