The following table lists the values of functions $${g}$$ and $${h}$$, and of their derivatives, $${g}^{\prime}$$ and $${h}^{\prime}$$, for the $${x}$$-values $$-2$$ and $$3$$. ![](http://admin.getprephub.com/media/editor/d115_20221016183226062758.png) Evaluate $$\frac{d}{d x}[g(h(x))]$$ at $$x=-2$$

Given that, $$\frac{d}{d x}[g(h(x))]=g^{\prime}(h(x)) h^{\prime}(x) $$ $$ \frac{d}{d x}[g(h(-2)]=g^{\prime}(h(-2)) h^{\prime}(-2). $$ $$ =g^{\prime}(3)\cdot(-5) $$ $$ =1 \cdot(-5) $$ $$ =-5 $$

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

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

$-5$

$5$

$6$

$-6$

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