Hi, I'm new to these forums so not exactly sure where to place this question, although calculus seems a good bet, so here goes:(adsbygoogle = window.adsbygoogle || []).push({});

I'm currently taking a mechanics course at my university (current subject is work/energy), and I'll just post this snippit from our textbook (Physics for Scientists and Engineers with Modern Physics 7th edition, Jewett/Serway):

[snippit]

[tex]

\begin{equation*}

W_{net}=\int^{x_f}_{x_i}\sum F\,dx

\end{equation*}

[/tex]

Using Newton's second law, we substitute for the magnitude of the net force [itex]\sum F=ma[/itex] and then perform the following chain-rule manipulations on the integrand:

[tex]

\begin{align*}

W_{net}&=\int^{x_f}_{x_i}ma\,dx=\int^{x_f}_{x_i}m\frac{dv}{dt}\,dx=\int^{x_f}_{x_i}m\frac{dv}{dx}\frac{dx}{dt}\,dx=\int^{v_f}_{v_i}mv\,dv\\

W_{net}&=\frac{1}{2}{mv_f}^2-\frac{1}{2}{mv_i}^2

\end{align*}

[/tex]

[/snippit]

How is:

[tex]\frac{dv}{dt}=\frac{dv}{dx}\frac{dx}{dt}[/tex]

legal in this context?

I know the Chain Rule states the following:

[tex]

\begin{equation*}

\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}

\end{equation*}

[/tex]

But this is valid only (to my understanding) for the derivative of the composite of two functions.

If anyone could help me sort this out, I'd be much obliged.

Thanks.

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# Chain rule / acceleration

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