$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$ $\sin x + 7 \cos 14 y = 2$
A) $\frac { d y } { d x } = \frac { \cos x } { 98 \cos 14 y }$
B) $\frac { d y } { d x } = \frac { \cos x } { 98 \sin 14 y }$
C) $\frac { d y } { d x } = \frac { \cos x } { 14 \sin 14 y }$
D) $\frac { d y } { d x } = \frac { \cos x } { 98 \sin y }$
E) $\frac { d y } { d x } = - \frac { \cos x } { 98 \sin 14 y }$

Question

Quizplus · Accepted Answer

We take the derivative of both sides with respect to x, using the chain rule on the left-hand side:

\begin{align*}
\frac{d}{dx}(\sin x + 7\cos(14y)) &= \frac{d}{dx}(2) \
\cos x - 98\sin (14y)\cdot\frac{dy}{dx} &= 0
\end{align*}

Solving for $\frac{dy}{dx}$, we get:

$$\frac{dy}{dx} = \frac{\cos x}{98\sin(14y)}$$

Therefore, the answer is (B).

Find dydx by implicit differentiation. \text { Find } \frac { d y } { d x } \text { by implicit differentiation. } Find dxdy​ by implicit differentiation.

$\text { Find } \frac { d y } { d x } \text { by implicit differentiation. }$