Question

If $2y={\sin }^{-1}(x+5y)$, then $\frac{dy}{dx}$ is equal to

• A. $\cos 2y–5$
• B. $\cos 2y+5$
• C. $\frac{1}{(2\cos 2y–5)}$
• D. None of these

Answer 1

The correct option is C

$\frac{1}{(2\cos 2y–5)}$

Explanation for the correct option:

Find the value of $\frac{dy}{dx}$:

Given, $2y={\sin }^{-1}(x+5y)$

$\Rightarrow$$\sin 2y=(x+5y)$

Differentiate it with respect to $x$:

$2\cos 2y\frac{dy}{dx}=1+5\frac{dy}{dx}$

$\Rightarrow$$\frac{dy}{dx}(2\cos 2y–5)=1$

$\Rightarrow$ $\frac{dy}{dx}=\frac{\mathbf{1}}{\mathbf{(}\mathbf{2}\mathbf{}\mathbf{c}\mathbf{o}\mathbf{s}\mathbf{}\mathbf{2}\mathbf{y}\mathbf{}\mathbf{–}\mathbf{}\mathbf{5}\mathbf{)}}$

Hence, Option ‘C’ is Correct.