Question

The derivative of $2 x+3 y=\sin y$ is

• A. $\frac{2}{\cos y}$
• B. $\frac{2}{\cos y+3}$
• C. $\frac{2}{\cos y-3}$
• D. None of these

Answer 1

Answer: (C)

Given, $2 x+3 y=\sin y$
On differentiating both sides w.r.t. $x$, we get
$\frac{d}{d x}(2 x+3 y)=\frac{d}{d x}(\sin y) $
$\Rightarrow 2+3 \frac{d y}{d x}=\cos y \frac{d y}{d x} $
$\Rightarrow 3 \frac{d y}{d x}-\cos y \frac{d y}{d x}=-2 $
$\Rightarrow (3-\cos y) \frac{d y}{d x}=-2$
$ \Rightarrow \frac{d y}{d x}=\frac{2}{\cos y-3}$