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# 复习：乘积法则

## 什么是乘法定则？

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

## 乘法定则可以解决哪些问题呢?

### 看看你的知识掌握地如何

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

### 例题 2

$x$$f\left(x\right)$$g\left(x\right)$${f}^{\prime }\left(x\right)$${g}^{\prime }\left(x\right)$
$4$$-4$$13$$8$
$H\left(x\right)$的定义是 $f\left(x\right)\cdot \left(x\right)$，我们被要求找到 ${H}^{\prime }\left(4\right)$

$\begin{array}{rl}{H}^{\prime }\left(4\right)& ={f}^{\prime }\left(4\right)g\left(4\right)+f\left(4\right){g}^{\prime }\left(4\right)\\ \\ & =\left(0\right)\left(13\right)+\left(-4\right)\left(8\right)\\ \\ & =-32\end{array}$

### 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$$2$$-1$$3$$4$
$F\left(x\right)=g\left(x\right)\cdot h\left(x\right)$
${F}^{\prime }\left(-2\right)=$