If H ( θ ) = θ cos ⁡ ( θ ), find H ′ ( θ ) and H ″ ( θ ).

Question

If   H  (  θ  )      ﻿    =  θ  cos  ⁡  (  θ  ), find       H    ′    (  θ  ) and       H    ″    (  θ  ).

Desirae Wu · Accepted Answer

H  (  θ  )  =  θ  cos  ⁡  θ      H    ′    (  θ  )  =      d          d      θ        (  θ  cos  ⁡  θ  )  =  θ  (  −  sin  ⁡  θ  )  +  cos  ⁡  θ  =  −  θ  sin  ⁡  θ  +  cos  ⁡  θ      H    ″    (  θ  )  =      d          d      θ        (      H    ′    (  θ  )  )  =      d          d      θ        (  −  θ  sin  ⁡  θ  )  +      d          d      θ        (  cos  ⁡  θ  )  =  −  [  θ  cos  ⁡  θ  +  sin  ⁡  θ  ]  −  sin  ⁡  t  h  e  t  a  =  −  θ  cos  ⁡  θ  −  sin  ⁡  θ  −  sin  ⁡  θ  =  −  θ  cos  ⁡  θ  −  2  sin  ⁡  θ

If H(theta)=theta cos (theta), find H'(theta) and H''(theta)

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