## 2020年8月6日木曜日

### 数学 - 解析学 - ベクトルの微分 - 微分係数 - 曲線、指数関数、三角関数(余弦)、内積、速度ベクトル、加速度ベクトル、速さ

1. $X\left(t\right)·B={e}^{2t}$
$\frac{d}{\mathrm{dt}}X\left(t\right)·B=\frac{d}{\mathrm{dt}}{e}^{2t}$
$X\text{'}\left(t\right)·B=2{e}^{2t}$
$\parallel X\text{'}\left(t\right)\parallel \parallel B\parallel \mathrm{cos}\theta =2{e}^{2t}$
$\parallel X\text{'}\left(t\right)\parallel \mathrm{cos}\theta =2{e}^{2t}$
$\parallel X\text{'}\left(t\right)\parallel =\frac{2{e}^{2t}}{\mathrm{cos}\theta }$

2. ${\parallel X\text{'}\left(t\right)\parallel }^{2}=\frac{4{e}^{4t}}{{\mathrm{cos}}^{2}\theta }$
$X\text{'}\left(t\right)·X\text{'}\left(t\right)=\frac{4{e}^{4t}}{{\mathrm{cos}}^{2}\theta }$
$\frac{d}{\mathrm{dt}}\left(X\text{'}\left(t\right)·X\text{'}\left(t\right)\right)=\frac{d}{\mathrm{dt}}\frac{4{e}^{4t}}{{\mathrm{cos}}^{2}\theta }$
$2X\text{'}\left(t\right)·X\text{'}\text{'}\left(t\right)=\frac{16{e}^{4t}}{{\mathrm{cos}}^{2}\theta }$
$X\text{'}\left(t\right)·X\text{'}\text{'}\left(t\right)=\frac{8{e}^{4t}}{{\mathrm{cos}}^{2}\theta }$