$$\text { Find } \frac { d y } { d x }$$
-$\sin y = 4 x + 2 y$
A) $\frac { 1 } { \sin y - 2 }$
B) $\frac { 4 } { \cos y - 2 }$
C) $\frac { 4 + 2 } { \cos y }$
D) $4 + 2 - \cos y$

Question

Quizplus · Accepted Answer

Step 1: Apply implicit differentiation to both sides of the equation with respect to x.
$$\frac { d } { d x } ( \sin y ) = \frac { d } { d x } ( 4 x + 2 y )$$
$$\cos y \cdot \frac{dy}{dx} =4+2\cdot \frac{dy}{dx}$$
$$(2+\cos y )\frac{dy}{dx}=4$$
$$\frac { dy } { dx } = \frac { 4 } { 2 + \cos y } =\frac { 4 } {\cos y +2}-\frac { 4 } { 2 } \cdot \frac { 1 } { \cos y+2 }$$
$$\frac { dy } { dx } = 2-\frac { 2 } { \cos y +2}$$
$$\frac { dy } { dx } =\frac { 4 } { \cos y -2 }$$

Find dydx\text { Find } \frac { d y } { d x } Find dxdy​

$\text { Find } \frac { d y } { d x }$