How take derivative d/dt(sinx), but have result be cosx * d/dt(x) ?

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Hello. I'd like to take a derivative of a function, sin(x). I have defined xDot as a symbol (the temporal derivative of x).
However, when I take d/dt (sinx) through
diff(sin(x), t, 1)
, I get 0. I want to have the returned expression be cos(x)*d/dt(x). How can I do this?

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