Question

If H(θ) = θ sin θ, find H'(θ) and H''(θ).

Answer 1

\[H(\theta)'=\theta(sin(\theta))'+sin(\theta)(\theta)'\]
\[H(\theta)'=\theta(-cos(\theta)(\theta)')+sin(\theta)\]
\[H(\theta)'=-\theta cos(\theta)+sin(\theta)\]

Answer 2

\[H(\theta)'=\theta(sin(\theta))'+sin(\theta)(\theta)'\]
\[H(\theta)'=\theta(cos(\theta)(\theta)')+sin(\theta)\]
\[H(\theta)'=\theta cos(\theta)+sin(\theta)\]

Answer 3

\[H(\theta)"=(\theta(cos(\theta))')+cos(\theta)(\theta)')+(sin(\theta))'\]
\[H(\theta)"=(\theta(-sin(\theta)(\theta)')+cos(\theta))+(cos(\theta)(\theta)')\]
\[H(\theta)"=-\theta sin(\theta)+cos(\theta))+cos(\theta)\]
\[H(\theta)"=-\theta sin(\theta)+2cos(\theta))\]

Answer 4

it is late where I'm at so you might want to check those answers with wolframalpha.com first