You drag a trunk of mass m across a level floor using a massless rope that makes an angle with the horizontal. Given a kinetic-friction coefficient (μ), Find the minimum force needed to move the trunk with constant speed. Do not answer in terms of theta; essentially, if you were allowed to vary the angle at which you pull the trunk, what is the minimum force required?

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You drag a trunk of mass m across a level floor using a massless rope that makes an angle with the horizontal. Given a kinetic-friction coefficient (μ), Find the minimum force needed to move the trunk with constant speed. Do not answer in terms of theta; essentially, if you were allowed to vary the angle at which you pull the trunk, what is the minimum force required?

Physics
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Welches Thema ist das genau ?
your exercise can be represented by this drawing: |dw:1443890056456:dw|
now, your trunk will move by uniform rectilinear motion if and only if the subsequent condition holds: \[\huge F\cos \theta = \mu \left( {mg - F\sin \theta } \right)\] where \(g=gravity\), \(\mu\) is the friction, and \(m\) is the mass of trunk. Solving for \(F\) we get: \[\huge F = \frac{{\mu mg}}{{\cos \theta + \mu \sin \theta }}\] Next you can try to minimize that quantity, using calculus, namely you have to solve this equation: \[\huge \frac{{\partial F}}{{\partial \theta }} = 0\]

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thank you so much!
although, I'm still not quite sure how to solve for the dF/dtheta

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