The following table lists the values of functions $${f}$$ and $${h}$$, and of their derivatives, $${f}^{\prime}$$ and $${h}^{\prime}$$ for the $${x}$$-values $$0$$ and $$2$$. ![](http://admin.getprephub.com/media/editor/d113_20221016183023442867.png) Evaluate $$\frac{d}{d x}[f(h(x))]$$ at $$x=0$$.

Here, $$\frac{d}{d x}[f(h(x))] =f^{\prime}(h(x))h^{\prime}(x).$$ $$\therefore \frac{d}{d x}[f(h(0))] =f^{\prime}(h(0)) h^{\prime}(0) $$ $$=f^{\prime}(2) \times(-3) $$ $$=3 \cdot(-3) $$ $$=-9$$

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The following table lists the values of functions ${f}$ and ${h}$ , and of their derivatives, ${f}^{\prime}$ and ${h}^{\prime}$ for the ${x}$ -values $0$ and $2$ .

Evaluate $\frac{d}{d x}[f(h(x))]$ at $x=0$ .

$-9$

$10$

$9$

$-10$

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