Differentiate with respect to t. y = d cos(t) + t² sin(t)

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}

Differentiate with respect to t. y = d cos(t) + t2 sin(t)

Summary:

Differentiating with respect to t for y = d cos(t) + t² sin(t), we get t²cos(t) + sin(t){2t - 1}