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So this time we're going to find the derivative in terms of
Theta.
So we're going to take DD Theta of cotangent of the quantity R
Theta squared equaling DD Theta of 1/7.
The derivative of cotangent is negative cosecant squared, R
Theta squared.
But now we have to do the chain rule.
So we need the derivative in terms of Theta of the R Theta
squared.
Derivative of a constant is 0.
So now once we do the derivative of our R Theta squared, we've
got to use the product rule.
So the derivative of R in terms of Theta times Theta squared
plus the derivative of Theta squared in terms of Theta times
R.
So we get negative cosecant squared R Theta squared times
the derivative of R in terms of Theta is 1D rural delivery Theta
times the Theta squared plus the derivative of Theta squared in
terms of Theta is going to be two Theta D Theta D Theta D
Theta D Theta is really just one times the R equaling 0.
So distributing that out, we get negative Theta squared, cosecant
squared R Theta squared DRD Theta -2 Theta R cosecant
squared R Theta squared equaling 0.
Going to take everything with a DRD Theta to one side and
everything else to the other.
Then we're going to divide.
So we get the DRD Theta by itself.
Next we're going to cancel.
So as we cancel, we're going to get -2 R over Theta.
We never leave a negative in the denominator.