What Is Wrong with This Differentiation?

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SUMMARY

The discussion revolves around a mathematical differentiation issue involving complex numbers and their application in calculus. The user initially defines \( t = jx \) where \( j = \sqrt{-1} \) and derives \( \frac{dt}{dx} = j \). However, a subsequent substitution using \( t^2 = -x^2 \) leads to a conflicting result of \( \frac{dt}{dx} = -\frac{x}{t} \). The confusion arises from the manipulation of complex variables and the implications of substituting back into the original equations.

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yungman
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I am confuse with this:

[tex]Let\;\; t=jx \;\;,\;\; j =\sqrt{-1}[/tex]

[tex]\Rightarrow \frac{dt}{dx}=j[/tex]

But if I use [tex]t^2=-x^2 \;\Rightarrow\; 2t\frac{dt}{dx}=-2x[/tex]

[tex]\Rightarrow \frac{dt}{dx}=-\frac{x}{t}[/tex]

What is wrong?
 
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sub back t=jx, and then multiply by j/j
 
rock.freak667 said:
sub back t=jx, and then multiply by j/j

Nice!

Thanks
 

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