If y = frac{cos 6x + 6cos 4x + 15cos 2x + 10} | vedclass

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Question

(B) Let the numerator be $N = \cos 6x + 6\cos 4x + 15\cos 2x + 10$. We can rewrite the coefficients using binomial expansion properties: $N = \cos 6x

Vedclass · Accepted Answer

$-2 \sin x$

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(B) Let the numerator be $N = \cos 6x + 6\cos 4x + 15\cos 2x + 10$. We can rewrite the coefficients using binomial expansion properties: $N = \cos 6x + \cos 4x + 5\cos 4x + 5\cos 2x + 10\cos 2x + 10$. Using the identity $\cos A + \cos B = 2\cos(\frac{A+B}{2})\cos(\frac{A-B}{2})$ and $1 + \cos 2x = 2\cos^2 x$: $N = 2\cos 5x \cos x + 5(2\cos 3x \cos x) + 10(2\cos^2 x)$. $N = 2\cos x (\cos 5x + 5\cos 3x + 10\cos x)$. Let the denominator be $D = \cos 5x + 5\cos 3x + 10\cos x$. Then $y = \frac{N}{D} = \frac{2\cos x (\cos 5x + 5\cos 3x + 10\cos x)}{\cos 5x + 5\cos 3x + 10\cos x} = 2\cos x$. Therefore,$\frac{dy}{dx} = \frac{d}{dx}(2\cos x) = -2\sin x$.

If $y = \frac{\cos 6x + 6\cos 4x + 15\cos 2x + 10}{\cos 5x + 5\cos 3x + 10\cos x}$,then $\frac{dy}{dx} = $

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