Question

Find the derivative of the given function. r = t² tan 0.5t.
dr/dt =

Answer 1

The derivative of the function r(t) = t^2 tan(0.5t) is dr/dt = 2t * tan(0.5t) + 0.5t^2sec^2(0.5t).

Step-by-step explanation:

The derivative of the given function r(t) = t^2 tan(0.5t) is obtained using the product rule. Let's break it down step by step:
1. Differentiate t^2: (t^2)' = 2t
2. Differentiate tan(0.5t): (tan(0.5t))' = 0.5sec^2(0.5t)
3. Apply the product rule: (r(t))' = (t^2)'(tan(0.5t)) + (t^2)(tan(0.5t))'
4. Simplify using the above derivatives: (r(t))' = 2t * tan(0.5t) + t^2 * 0.5sec^2(0.5t)
Thus, the derivative of r(t) = t^2 tan(0.5t) is dr/dt = 2t * tan(0.5t) + 0.5t^2sec^2(0.5t).