微積分驗算 1.3

這段改編自 2010 年 6 月 2 日的對話。

又再例如,求 d/dx (1/sqrt{x}) 時,你直接計算了以後,可以同時用「消滅分母法」和「消滅開方法」去驗算:

y = 1/sqrt{x}

y^2 = 1/x

x y^2 = 1

左右兩邊同時對 x 求導:

(Differentiate both sides with respect to x:)

(dx/dx) y^2 + x d/dx (y^2) = d(1)/dx

y^2 + x 2 y dy/dx = 0

2 x y dy/dx = – y^2

dy/dx = – y/(2x)

dy/dx = – (1/sqrt{x})/(2x)

dy/dx = – 1/(2 x sqrt{x})

— Me@2012.04.28

2012.04.28 Saturday (c) All rights reserved by ACHK