Answer
$$\frac{dy}{dt}=-2\cos(\cos(2t-5))\sin(2t-5)$$
Work Step by Step
$$\frac{dy}{dt}=\frac{d}{dt}(\sin(\cos(2t-5)))$$
Following the Chain Rule: $$\frac{dy}{dt}=\cos(\cos(2t-5))\frac{d}{dt}(\cos(2t-5))$$
$$\frac{dy}{dt}=\cos(\cos(2t-5))(-\sin(2t-5))\frac{d}{dt}(2t-5)$$
$$\frac{dy}{dt}=-\cos(\cos(2t-5))\sin(2t-5)(2\times1-0)$$
$$\frac{dy}{dt}=-2\cos(\cos(2t-5))\sin(2t-5)$$
