Contextual Applications of Differentiation · Challenge problem

A slider-crank mechanism has a crank of radius $3$ cm rotating at $4$ rad/s, connected to a piston by a rod of length $5$ cm. The piston's position is $x(\theta)=3\cos\theta+\sqrt{25-9\sin^2\theta}$. Find the piston's velocity $\dfrac{dx}{dt}$, in cm/s, at the instant $\theta=90^\circ$.