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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

$-2 \sin x$

Vedclass · Answer

(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} = $

Similar Questions

The differential coefficient of the function $|x - 1| + |x - 3|$ at the point $x = 2$ is

If $f(x) = \frac{1}{1 + \frac{1}{x}}$ and $g(x) = \frac{1}{1 + \frac{1}{f(x)}}$, then $g^{\prime}(2)$ is equal to

If $f(x)=|x-1|+|x-2|$, then $f^{\prime}(-2023)+f^{\prime}\left(\frac{2024}{2023}\right)+f^{\prime}(2023)=$

Let $f: R \rightarrow R$ be a function such that $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+6, x \in R$,then $f(2)$ equals

Find the derivative of $x^{-3}(5+3x)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module