Suppose you have a function x(t)=ct^2. Then you are asked to compute dx'/dx, where x' denotes a derivative to time; x'=dx/dt.(adsbygoogle = window.adsbygoogle || []).push({});

I: [tex] \frac{dx'}{dx}=\frac{d}{dx} \frac{dx}{dt} =\frac{d}{dt} \frac{dx}{dx}= \frac{d}{dt}(1)=0 [/tex] (By using Clairaut's theorem)

II: [tex]x'=2ct=2c \sqrt{\frac{x}{c}}=2 \sqrt{cx} -> \frac{dx'}{dx}=\frac{d}{dx} 2 \sqrt{cx} = \sqrt{\frac{c}{x}}[/tex]

Can someone clarify this for me?

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# Differentiation paradox?

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