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With respect to?
If the derivative of theta is 1, it has to be in respect to theta
The question asks me to find the derivative of H(theta)= thetasintheta
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if with respect to theta, yes it's 1.
Nicole, I don't really understand the question you have. Could to rephase it at all?
it says: If H(theta)= thetas(sin theta), find H'(theta) and H"(theta)
Yeah, just do it the standard way.
If the question is H(Ø) = Øsin(Ø) and you're differentiating with respect to Ø, then you'd have to use the Product Rule here since you have one variable quantity, Ø, being multiplied by another variable quantity, sin(Ø). Thus...
H(Ø) = Øsin(Ø)
H'(Ø) = (1)(sin(Ø)) + (Ø)(cos(Ø)) = sin(Ø) + Øcos(Ø)
H''(Ø) = cos(Ø) + (1)(cos(Ø)) + (Ø)(–sin(Ø)) = 2cos(Ø) – Øsin(Ø)
Unless the question also gave you an initial condition or a value for Ø to plug in to the original function and/or its derivatives, I'm not very sure where the value of 1 came into the picture.