If $4 x + e ^ { 3 x y } = 9 , \text { find } d y / d x$
A) $\frac { d y } { d x } = - \frac { 4 + 3 y e ^ { 3 xy } } { 3 x e ^ { 3 xy } }$
B) $\frac { d y } { d x } = - \frac { 4 + 3 x e ^ { 3 xy } } { 3 y e ^ { 3 xy } }$
C) $\frac { d y } { d x } = \frac { 4 + 3 y e ^ { 3 x y } } { 4 x e ^ { 3 xy } }$
D) $\frac { d y } { d x } = \frac { 4 + 3 x e ^ { 3 x y } } { 3 y e ^ { 3 x y } }$
E) $\frac { d y } { d x } = \frac { 4 + 3 y e ^ { 3 x y } } { x e ^ { 3 x y } }$

Question

Quizplus · Accepted Answer

To find $dy/dx$, we differentiate both sides of the equation $4x + e^{3xy} = 9$ with respect to $x$, applying the chain rule for $e^{3xy}$. Differentiating $4x$ gives $4$, and for $e^{3xy}$, we get $3ye^{3xy}$ times the derivative of $3xy$ with respect to $x$, which is $3y$. Setting the derivative of the left side equal to the derivative of the constant $9$ (which is $0$) and solving for $dy/dx$ gives the correct formula.

If 4x+e3xy=9, find dy/dx4 x + e ^ { 3 x y } = 9 , \text { find } d y / d x4x+e3xy=9, find dy/dx

If $4 x + e ^ { 3 x y } = 9 , \text { find } d y / d x$