# 微分的線性

## 說明

fg 為函數，同時 αβ 是常數，思考：

${\displaystyle {\frac {\mbox{d}}{{\mbox{d}}x}}(\alpha \cdot f(x)+\beta \cdot g(x))}$

${\displaystyle {\frac {\mbox{d}}{{\mbox{d}}x}}(\alpha \cdot f(x))+{\frac {\mbox{d}}{{\mbox{d}}x}}(\beta \cdot g(x))}$

${\displaystyle \alpha \cdot f'(x)+\beta \cdot g'(x)}$

${\displaystyle {\frac {\mbox{d}}{{\mbox{d}}x}}(\alpha \cdot f(x)+\beta \cdot g(x))=\alpha \cdot f'(x)+\beta \cdot g'(x)}$

${\displaystyle (\alpha \cdot f+\beta \cdot g)'=\alpha \cdot f'+\beta \cdot g'}$

## 參考資料

1. ^ Blank, Brian E.; Krantz, Steven George, Calculus: Single Variable, Volume 1, Springer: 177, 2006, ISBN 9781931914598.
2. ^ Strang, Gilbert, Calculus, Volume 1, SIAM: 71–72, 1991, ISBN 9780961408824.
3. ^ Stroyan, K. D., Calculus Using Mathematica, Academic Press: 89, 2014, ISBN 9781483267975
4. ^ Estep, Donald, 20.1 Linear Combinations of Functions, Practical Analysis in One Variable, Undergraduate Texts in Mathematics, Springer: 259–260, 2002, ISBN 9780387954844.
5. ^ Zorn, Paul, Understanding Real Analysis, CRC Press: 184, 2010, ISBN 9781439894323.
6. ^ Gockenbach, Mark S., Finite-Dimensional Linear Algebra, Discrete Mathematics and Its Applications, CRC Press: 103, 2011, ISBN 9781439815649.