Problem 85E

85. (a) If $n$ is a positive integer, prove that

$$ \frac{d}{d x}\left(\sin ^{n} x \cos n x\right)=n \sin ^{n-1} x \cos (n+1) x $$

(b) Find a formula for the derivative of $y=\cos ^{n} x \cos n x$ that is similar to the one in part (a).

 

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