The following table lists the values of functions $g$ and $h$ , and of their derivatives, $g^{'}$ and $h^{'}$ , for the $x$ -values -2 and 3 .
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Evaluate $\frac{d}{d x} [g (h (x))]$ at $x = - 2$

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Answer

$f^{'} (- 2) = - 5$ is the derivative of $g (h (x))$ at $x = - 2$ .

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Step 1 ：Let $f (x) = g (h (x))$ , then the derivative $f^{'} (x)$ is given by $f^{'} (x) = g^{'} (h (x)) \cdot h^{'} (x)$ using the chain rule.

Step 2 ：Substitute $x = - 2$ into the equation to get $f^{'} (- 2) = g^{'} (h (- 2)) \cdot h^{'} (- 2)$ .

Step 3 ：From the table, we know that $h (- 2) = 3$ and $h^{'} (- 2) = - 5$ . So, substitute these values into the equation to get $f^{'} (- 2) = g^{'} (3) \cdot - 5$ .

Step 4 ：Again from the table, we know that $g^{'} (3) = 1$ . So, substitute this value into the equation to get $f^{'} (- 2) = 1 \cdot - 5 = - 5$ .

Step 5 ： $f^{'} (- 2) = - 5$ is the derivative of $g (h (x))$ at $x = - 2$ .

The following table lists the values of functions g and h, and of their derivatives, g′ and h′, for the x-values -2 and 3 .Unknown environment 'tabular'Unknown environment 'tabular' Evaluate ddx[g(h(x))] at x=−2

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The following table lists the values of functions $g$ and $h$ , and of their derivatives, $g^{'}$ and $h^{'}$ , for the $x$ -values -2 and 3 .
$Unknown environment 'tabular'$

Evaluate $\frac{d}{d x} [g (h (x))]$ at $x = - 2$