# polyder

## 语法

``k = polyder(p)``
``k = polyder(a,b)``
``[q,d] = polyder(a,b)``

## 说明

``k = polyder(p)` 返回 `p` 中的系数表示的多项式的导数，$k\left(x\right)=\frac{d}{dx}p\left(x\right)\text{\hspace{0.17em}}.$`

``k = polyder(a,b)` 返回多项式 `a` 和 `b` 的乘积的导数，$k\left(x\right)=\frac{d}{dx}\left[a\left(x\right)b\left(x\right)\right]\text{\hspace{0.17em}}.$`

``[q,d] = polyder(a,b)` 返回多项式 `a` 和 `b` 的商的导数，$\frac{q\left(x\right)}{d\left(x\right)}=\frac{d}{dx}\left[\frac{a\left(x\right)}{b\left(x\right)}\right]\text{\hspace{0.17em}}.$`

## 示例

`p = [3 0 -2 0 1 5];`

`q = polyder(p)`
```q = 1×5 15 0 -6 0 1 ```

```a = [1 -2 0 0 11]; b = [1 -10 15];```

`$q\left(x\right)=\frac{d}{dx}\left[a\left(x\right)b\left(x\right)\right].$`

`q = polyder(a,b)`
```q = 1×6 6 -60 140 -90 22 -110 ```

`$q\left(x\right)=6{x}^{5}-60{x}^{4}+140{x}^{3}-90{x}^{2}+22x-110.$`

`$\frac{{x}^{4}-3{x}^{2}-1}{x+4}.$`

```p = [1 0 -3 0 -1]; v = [1 4];```

`$\frac{q\left(x\right)}{d\left(x\right)}=\frac{d}{dx}\left[\frac{p\left(x\right)}{v\left(x\right)}\right].$`

`[q,d] = polyder(p,v)`
```q = 1×5 3 16 -3 -24 1 ```
```d = 1×3 1 8 16 ```

`$\frac{q\left(x\right)}{d\left(x\right)}=\frac{3{x}^{4}+16{x}^{3}-3{x}^{2}-24x+1}{{x}^{2}+8x+16}.$`