Find the derivative of  using two different methods.

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Solution:

Method One (The Chain Rule):

Method Two (The Product Rule):

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Calculus II (BC): Polar Derivatives

Find all angles which result in points of horizontal tangency to the polar equation .

 

Difficulty Rating: 

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Solution: We first need to find the derivative of the polar function by converting to rectanglar mode. Then, we can find dy/dx by finding the indicated quotient. Knowing that the numerator of a derivative equalling zero results in a horizontal point of tangency, we set the numerator equal to zero and get the correct thetas. The actual work is as follows:

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