How can I find "dx" in a straight line of electric charge?(Picture)

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SUMMARY

The discussion centers on the derivation of the equation dx = R/cos²(θ) dθ in the context of electric charge along a straight line. The user initially struggled to understand this relationship but ultimately clarified their misunderstanding regarding the differentiation of x = R tan(θ). The resolution highlights the importance of correctly applying trigonometric identities and differentiation techniques in physics problems involving electric fields.

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MatinSAR
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Homework Statement
How can I find "dx" in a straight line of electric charge?(Details in Picture)
Relevant Equations
r=R/cos(teta)
x=rtan(teta)
1646478251956.png

This is the question ... I have it's solution ...
1646478322100.png

1646478364142.png
My problem : I can't understand why dx=R/cos^2(teta) dteta
I have thought many hours but I couldn't find it's reason ... Can anyone please help with this ?!
 
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If ##x = R\tan{\theta}##, then ##dx/d\theta= \dots##
 
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ergospherical said:
If ##x = R\tan{\theta}##, then ##dx/d\theta= \dots##
I got it ... I have learned this in a wrong way but now I know what was wrong ... Thanks a lot 🌷
 
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Likes   Reactions: vanhees71 and jim mcnamara

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