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## Main Question or Discussion Point

OK, I lied a bit. It's not JUST the derivative of an integral. It's the derivative of a cosine of an integral. Solving the problem of the motion of a simple pendulum under a gravitational field using the lagrangian, I came into this mess (which I don't know if it's right):

l^2*((dθ/dt)/dt)-mg*d(cosθ)/(dθ/dt)=dL/dθ

The part I want to focus on is d(cosθ)/(dθ/dt). I know d(cosθ) is not a constant, because it depends on dθ/dt, since it's its integral with respect to dt, but how do I find what it is?

l^2*((dθ/dt)/dt)-mg*d(cosθ)/(dθ/dt)=dL/dθ

The part I want to focus on is d(cosθ)/(dθ/dt). I know d(cosθ) is not a constant, because it depends on dθ/dt, since it's its integral with respect to dt, but how do I find what it is?