Consider the equation $\ln | y / ( 1 - y ) | = 0.34 x + \ln 4$ .Assuming this implicitly defines y as a function of x, find $\frac { d y } { d x }$ .
A) $0.34 y ( 1 - y )$
B) $0.34 y / ( 1 - y )$
C) $0.34 y$
D) $- 0.34 y ( 1 - y )$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$, differentiate both sides of the equation with respect to $x$. Using the chain rule, the left side becomes $\frac{1}{y/(1-y)} \cdot \frac{d}{dx}[y/(1-y)] = \frac{1-y+y'}{y(1-y)}$, where $y'$ is $\frac{dy}{dx}$. The right side becomes $0.34$. Setting these equal gives $0.34 = \frac{1-y+y'}{y(1-y)}$, solving for $y'$ yields $y' = 0.34y(1-y)$.

Consider the Equation ln⁡∣y/(1−y)∣=0.34x+ln⁡4\ln | y / ( 1 - y ) | = 0.34 x + \ln 4ln∣y/(1−y)∣=0.34x+ln4

Consider the Equation $\ln | y / ( 1 - y ) | = 0.34 x + \ln 4$