Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

derivative question?

Given the following transformation:

x/c = (1-cos(t))/2,

why is it equivalent of saying dx/c = sin(t)/2 dt ? I understand that sin(t)/2 comes from taking the derivative of the right hand side, but where does the dx and the dt come from?Thanks in advance :)

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  • 1 month ago
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    This is always the riddle we present calc students with - we tell them the d/dx is not a fraction and then in certain problems, we treat it like a fraction.  So the "correct" way to think of this is you want to find the change in in t, dt, that cause a change in x, dx.  So we take the differential of both sides:

    dx/c = d(1-cos(t))/2/dt *dt = sin(t)/2 dt

    • David1 month agoReport

      Ah, I understand, so it is basicly taking the derivative on both sides and then multiplying again by dx on LHS and dt on RHS? If it were e.g. x^2/c, then we would have 2x/c dx on the RHS?  

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