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Solution:
Given y = d cos(t) + t2 sin(t)
Let us differentiate y w.r.t t
dy/dt = d cos(t)/dt + d(t2 sin(t))/dt
Since, d/dt (uv) = udv/dt + vdu/dt
Here u = t2 and v =sint
dy/dt = -sin(t) + {t2cos(t) + sin(t)2t}
dy/dt = t2cos(t) + sin(t){2t - 1}
Summary:
Differentiating with respect to t for y = d cos(t) + t2 sin(t), we get t2cos(t) + sin(t){2t - 1}