Use implicit differentiation to find dy/dx.
-$$\mathrm { e } ^ { 3 \mathrm { x } } = \sin ( \mathrm { x } + 2 \mathrm { y } )$$
A) $\frac { d y } { d x } = \frac { - 3 e ^ { x } } { \sin ( x + 2 y ) }$
B) $\frac { d y } { d x } = \frac { 3 e ^ { x } } { 2 \sin ( x + 2 y ) }$
C) $\frac { d y } { d x } = \frac { 6 e ^ { x } } { \sin ( x + 2 y ) }$
D) $\frac { d y } { d x } = - \frac { 3 e ^ { x } } { 2 \sin ( x + 2 y ) }$

Question

Quizplus · Accepted Answer

Implicit differentiation gives:$$3e^{3x}=\cos(x+2y)(1+2\frac{dy}{dx})$$$$3e^{3x}=\cos(x+2y)+2\cos(x+2y)\frac{dy}{dx}$$$$2\cos(x+2y)\frac{dy}{dx}=3e^{3x}-\cos(x+2y)$$$$\frac{dy}{dx}=\frac{3e^{3x}-\cos(x+2y)}{2\cos(x+2y)}$$$$\frac{dy}{dx}=\frac{3e^{3x}}{2\cos(x+2y)}-\frac{\cos(x+2y)}{2\cos(x+2y)}$$$$\frac{dy}{dx}=\frac{3e^{3x}}{2\sin(x+2y)}$$

Use Implicit Differentiation to Find Dy/dx e3x=sin⁡(x+2y)\mathrm { e } ^ { 3 \mathrm { x } } = \sin ( \mathrm { x } + 2 \mathrm { y } )e3x=sin(x+2y)

Use Implicit Differentiation to Find Dy/dx $\mathrm { e } ^ { 3 \mathrm { x } } = \sin ( \mathrm { x } + 2 \mathrm { y } )$