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

Solution:

y = b cos(t) + t² sin(t)

y is a function of t. ⇒ y = f(t)

Let us differentiate the above equation w.r.t t

Consider b cos(t)

d(b cos(t))/dt = b. d(cos t)/dt

= b(-sin t)

=-b sin t

Consider b cos(t)

We use the product rule to differentiate t² sin(t).

Here y = u(t) × v(t)

dy/ dt = u. dv/dt + v. du/dt

t² sin(t) =  t² (cos t) + sin t (2t)

dy/dt =-b sin t + t² (cos t) + sin t (2t)

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

Summary:

Differentiating y = b cos(t) + t² sin(t) with respect to t, we get dy/dt =-b sin t + t² (cos t) + sin t (2t)