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# 复习：除法定则

## 什么是商的求导法则?

$\frac{d}{dx}\left[\frac{f\left(x\right)}{g\left(x\right)}\right]=\frac{\frac{d}{dx}\left[f\left(x\right)\right]\cdot g\left(x\right)-f\left(x\right)\cdot \frac{d}{dx}\left[g\left(x\right)\right]}{\left[g\left(x\right){\right]}^{2}}$

## 商的求导法则可以解决哪些问题呢？

### 看看你的知识掌握地如何

$f\left(x\right)=\frac{{x}^{2}}{{e}^{x}}$
${f}^{\prime }\left(x\right)=$

### 例题 2

$x$$f\left(x\right)$$g\left(x\right)$${f}^{\prime }\left(x\right)$${g}^{\prime }\left(x\right)$
$4$$-4$$-2$$0$$8$
$H\left(x\right)$ 被定义为 $\frac{f\left(x\right)}{g\left(x\right)}$, 我们需要找到 ${H}^{\prime }\left(4\right)$.

$\begin{array}{rl}{H}^{\prime }\left(4\right)& =\frac{{f}^{\prime }\left(4\right)g\left(4\right)-f\left(4\right){g}^{\prime }\left(4\right)}{\left[g\left(4\right){\right]}^{2}}\\ \\ & =\frac{\left(0\right)\left(-2\right)-\left(-4\right)\left(8\right)}{\left(-2{\right)}^{2}}\\ \\ & =\frac{32}{4}\\ \\ & =8\end{array}$

### 看看你的知识掌握地如何

$x$$g\left(x\right)$$h\left(x\right)$${g}^{\prime }\left(x\right)$${h}^{\prime }\left(x\right)$
$-2$$4$$1$$-1$$2$
$F\left(x\right)=\frac{g\left(x\right)}{h\left(x\right)}$
${F}^{\prime }\left(-2\right)=$