Differentiate with respect to t. y = a cos(t) + t²sin(t)

Solution:

Given expression is y = a cos(t) + t²sin(t)

Differentiate with respect to t, using the product rule.

dy/dt = d[acos(t)]/dt + d[t²sin(t)]/dt

= adcos(t)/dt + t²dsin(t)/dt + sin(t)d t²/dt

= a(-sint) + t²(cost) + sin(t) (2t)

= -asin(t) + t²Cos(t) + 2tsin(t)

= t²cos(t) + (2t - a)sin(t)

Differentiate with respect to t. y = a cos(t) + t²sin(t)

Summary:

Differentiating y = a cos(t) + t²sin(t) with respect to we have t²cos(t) + (2t - a)sin(t)