A table of values for f,g, f', and g' is given.xf(x)g(x)f′(x)g′(x)132462185737279a) If h(x)=f(g(x)), find h'(3)b) If H(x)=g(f(x)),find H'(1).

Given:To determine:a) h(x)=f(g(x))To find h'(3)h(x)=f(g(x))Then,h′(x)=f′(g(x))⋅g′(x)Putting x=3,h′(3)=f′(g(3))⋅g′(3)From the given table,g(3)=2 and g′(3)=9So, h′(3)=f′(2)⋅9From the table, f′(2)=5h′(3)=5⋅9h′(3)=45

b) H(x)=g(f(x))Then,H′(x)=g′(f(x))⋅f′(x)Putting x=1H′(1)=g′(f(1))⋅f′(1)From the given table, f(1)=3 and f′(1)=4H′(1)=9⋅4H′(1)=36

Given:To determine:a) h(x)=f(g(x))To find h'(3)h(x)=f(g(x))Then,h′(x)=f′(g(x))⋅g′(x)Putting x=3,h′(3)=f′(g(3))⋅g′(3)From the given table,g(3)=2 and g′(3)=9So, h′(3)=f′(2)⋅9From the table, f′(2)=5h′(3)=5⋅9h′(3)=45

b) H(x)=g(f(x))Then,H′(x)=g′(f(x))⋅f′(x)Putting x=1H′(1)=g′(f(1))⋅f′(1)From the given table, f(1)=3 and f′(1)=4H′(1)=9⋅4H′(1)=36

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skeexerxo175o

Answered question

2021-11-21

A table of values for f,g, f', and g' is given.

\begin{array}{cc} x & f (x) & g (x) & f^{'} (x) & g^{'} (x) \\ 1 & 3 & 2 & 4 & 6 \\ 2 & 1 & 8 & 5 & 7 \\ 3 & 7 & 2 & 7 & 9 \end{array}

a) If h(x)=f(g(x)), find h'(3)
b) If H(x)=g(f(x)),find H'(1).

Answer & Explanation

Lible1953

Beginner2021-11-22Added 16 answers

Given:
To determine:
a)

h (x) = f (g (x))

To find h'(3)

h (x) = f (g (x))

Then,

h^{'} (x) = f^{'} (g (x)) \cdot g^{'} (x)

Putting x=3,

h^{'} (3) = f^{'} (g (3)) \cdot g^{'} (3)

From the given table,

g (3) = 2

and

g^{'} (3) = 9

So,

h^{'} (3) = f^{'} (2) \cdot 9

From the table,

f^{'} (2) = 5

h^{'} (3) = 5 \cdot 9

h^{'} (3) = 45

Fearen

Beginner2021-11-23Added 15 answers

b) H(x)=g(f(x))
Then,
$H^{'} (x) = g^{'} (f (x)) \cdot f^{'} (x)$
Putting x=1
$H^{'} (1) = g^{'} (f (1)) \cdot f^{'} (1)$
From the given table, $f (1) = 3$ and $f^{'} (1) = 4$
$H^{'} (1) = 9 \cdot 4$
$H^{'} (1) = 36$

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