Quick question. I know that if we have a curve defined by ##x=f(t)## and ##y=g(t)##, then the slope of the tangent line is ##\displaystyle \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}##. I am trying to find the second derivative, which would be ##\displaystyle \frac{d}{dx}\frac{dy}{dx} = \frac{\frac{d}{dx}\frac{dy}{dt}}{\frac{dx}{dt}}##. Now, the final correct formula is ##\displaystyle \frac{d^2 y}{dx^2} = \frac{\frac{d}{dt}\frac{dy}{dx}}{\frac{dx}{dt}}##. My question is, why is it valid that ##\displaystyle \frac{d}{dx} \frac{dy}{dt} = \frac{d}{dt} \frac{dy}{dx}##?(adsbygoogle = window.adsbygoogle || []).push({});

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# I Second derivative of a curve defined by parametric equations

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