## 2017年2月10日金曜日

### 数学 - 解析学 - 微分法 - 微分法の諸公式

1. $3{\left(2{x}^{2}-2x+1\right)}^{2}\left(4x-2\right)$

2. $10{\left({x}^{2}+1\right)}^{9}2x\left(2x-5\right)+\left({x}^{2}+1\right)4\left(2x-5\right)2$

3. $\frac{\left(2x-2\right)\left({x}^{2}+x+2\right)-\left({x}^{2}-2x+6\right)\left(2x+1\right)}{{\left({x}^{2}+x+2\right)}^{2}}$

4. $\frac{3{\left(3x+2\right)}^{2}3\left(2x-1\right)-{\left(3x+2\right)}^{3}2\left(2x-1\right)2}{{\left(2x-1\right)}^{4}}$

5. $\frac{3}{2}{\left({x}^{2}+2x\right)}^{\frac{1}{2}}\left(2x+2\right)$

6. $\frac{\sqrt{2{x}^{2}-1}-x·\frac{1}{2}{\left(2{x}^{2}-1\right)}^{-\frac{1}{2}}4x}{2{x}^{2}-1}$

1. $\begin{array}{l}f\text{'}\left(x\right)=\sum _{i=1}^{n}\left(x-{\alpha }_{1}\right)···\left(x-{\alpha }_{i-1}\right)\left(x-{\alpha }_{i+1}\right)···\left(x-{\alpha }_{n}\right)\\ f\text{'}\left({a}_{k}\right)=\left(x-{\alpha }_{1}\right)···\left(x-{\alpha }_{k-1}\right)\left(x-{\alpha }_{k+1}\right)···\left(x-{\alpha }_{n}\right)\\ {A}_{k}=\frac{1}{\left(x-{\alpha }_{1}\right)···\left(x-{\alpha }_{k-1}\right)\left(x-{\alpha }_{k+1}\right)···\left(x-{\alpha }_{n}\right)}\\ \frac{{A}_{k}}{x-{\alpha }_{k}}=\frac{1}{\left(x-{\alpha }_{1}\right)···\left(x-{\alpha }_{n}\right)}=\frac{1}{f\left(x\right)}\\ \frac{n}{f\left(x\right)}=\sum _{k=1}^{n}\frac{{A}_{k}}{x-{\alpha }_{k}}\end{array}$