What is the difference between d/dt and dy/dt?
By John Campbell •
What is the difference between d/dt and dy/dt? And when should either be used? I have seen both in my calculus class and don't know which to use in what context.
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$\begingroup$$\frac d{dt}$ is the differential operator. It doesn't signify any particular value, it's just meant to be applied to functions.
If you apply that operator to the function $y=y(t)$, then you get $$\frac d{dt}y = \frac{dy}{dt}$$
Or you can apply it to both sides of an equation relating functions like: $$f(t) = t^2+1 \\ \implies \frac d{dt}f(t) = \frac{d}{dt}(t^2+1) \\ \implies \frac{df(t)}{dt} = 2t$$
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